{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T18:28:05Z","timestamp":1778351285575,"version":"3.51.4"},"reference-count":71,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2017,10,27]],"date-time":"2017-10-27T00:00:00Z","timestamp":1509062400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s10208-017-9372-x","type":"journal-article","created":{"date-parts":[[2017,10,27]],"date-time":"2017-10-27T18:37:05Z","timestamp":1509129425000},"page":"1435-1492","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Polynomial\u2013Exponential Decomposition From Moments"],"prefix":"10.1007","volume":"18","author":[{"given":"Bernard","family":"Mourrain","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,10,27]]},"reference":[{"key":"9372_CR1","unstructured":"Encyclopedia of Mathematics, April 2016."},{"key":"9372_CR2","doi-asserted-by":"crossref","unstructured":"Naum\u00a0I. Ahiezer and Mark\u00a0G. Kre\u012dn. Some Questions in the Theory of Moments. American Mathematical Society, Providence, 1962.","DOI":"10.1090\/mmono\/002"},{"issue":"3","key":"9372_CR3","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s00020-015-2217-6","volume":"82","author":"Fredrik Andersson","year":"2015","unstructured":"Fredrik Andersson and Marcus Carlsson. On General Domain Truncated Correlation and Convolution Operators with Finite Rank. Integral Equations and Operator Theory, 82(3):339\u2013370, 2015.","journal-title":"Integral Equations and Operator Theory"},{"key":"9372_CR4","doi-asserted-by":"crossref","unstructured":"Fredrik Andersson and Marcus Carlsson. On the structure of positive semi-definite finite rank general domain Hankel and Toeplitz operators in several variables. Complex Analysis and Operator Theory, 11(4):755\u2013784, 2017.","DOI":"10.1007\/s11785-016-0596-6"},{"issue":"2","key":"9372_CR5","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.acha.2009.09.001","volume":"29","author":"Fredrik Andersson","year":"2010","unstructured":"Fredrik Andersson, Marcus Carlsson, and Maarten\u00a0V. de\u00a0Hoop. Nonlinear approximation of functions in two dimensions by sums of wave packets. Appl. Comput. Harmon. Anal., 29(2):198\u2013213, 2010.","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9372_CR6","doi-asserted-by":"crossref","unstructured":"George\u00a0A. Baker and Peter Graves-Morris. Pad\u00e9 Approximants. Cambridge University Press, Cambridge England, New York, 2nd edition, 1996.","DOI":"10.1017\/CBO9780511530074"},{"key":"9372_CR7","first-page":"715","volume":"301","author":"Laurent Barachart","year":"1984","unstructured":"Laurent Barachart. Sur la r\u00e9alisation de Nerode des syst\u00e8mes multi-indiciels. C. R. Acad. Sc. Paris, 301:715\u2013718, 1984.","journal-title":"C. R. Acad. Sc. Paris"},{"issue":"1","key":"9372_CR8","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1137\/110836584","volume":"73","author":"Dmitry Batenkov","year":"2013","unstructured":"Dmitry Batenkov and Yosef Yomdin. On the accuracy of solving confluent Prony systems. SIAM Journal on Applied Mathematics, 73(1):134\u2013154, 2013.","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"1","key":"9372_CR9","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s00211-006-0054-x","volume":"106","author":"Bernhard Beckermann","year":"2007","unstructured":"Bernhard Beckermann, Gene\u00a0H. Golub, and George Labahn. On the numerical condition of a generalized Hankel eigenvalue problem. Numerische Mathematik, 106(1):41\u201368, 2007.","journal-title":"Numerische Mathematik"},{"issue":"3","key":"9372_CR10","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1137\/S0895479892230031","volume":"15","author":"Bernhard Beckermann","year":"1994","unstructured":"Bernhard Beckermann and George Labahn. A uniform approach for the fast computation of matrix-type Pad\u00e9 approximants. SIAM Journal on Matrix Analysis and Applications, 15(3):804\u2013823, 1994.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"9372_CR11","doi-asserted-by":"crossref","unstructured":"Michael Ben-Or and Prasson Tiwari. A deterministic algorithm for sparse multivariate polynomial interpolation. In Proceedings of the twentieth annual ACM symposium on Theory of computing, STOC \u201988, pages 301\u2013309, New York, NY, USA, 1988. ACM.","DOI":"10.1145\/62212.62241"},{"issue":"2","key":"9372_CR12","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1109\/TIT.1968.1054109","volume":"14","author":"Elwyn R Berlekamp","year":"1968","unstructured":"Elwyn\u00a0R. Berlekamp. Nonbinary BCH decoding. IEEE Transactions on Information Theory, 14(2):242\u2013242, 1968.","journal-title":"IEEE Transactions on Information Theory"},{"key":"9372_CR13","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.jsc.2012.05.012","volume":"52","author":"Alessandra Bernardi","year":"2013","unstructured":"Alessandra Bernardi, J\u00e9r\u00f4me Brachat, Pierre Comon, and Bernard Mourrain. General tensor decomposition, moment matrices and applications. Journal of Symbolic Computation, 52:51\u201371, 2013.","journal-title":"Journal of Symbolic Computation"},{"key":"9372_CR14","doi-asserted-by":"crossref","unstructured":"J\u00e9r\u00e9my Berthomieu, Brice Boyer, and Jean-Charles Faug\u00e8re. Linear Algebra for Computing Gr\u00f6bner Bases of Linear Recursive Multidimensional Sequences. In International Symposium on Symolic and Algebraic Compution, pages 61\u201368. ACM Press, 2015.","DOI":"10.1145\/2755996.2756673"},{"issue":"1","key":"9372_CR15","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.acha.2005.01.003","volume":"19","author":"Gregory Beylkin","year":"2005","unstructured":"Gregory Beylkin and Lucas Monz\u00f3n. On approximation of functions by exponential sums. Appl. Comput. Harmon. Anal., 19(1):17\u201348, 2005.","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9372_CR16","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1016\/j.laa.2010.06.046","volume":"433","author":"J\u00e9rome Brachat","year":"2010","unstructured":"J\u00e9rome Brachat, Pierre Comon, Bernard Mourrain, and Elias Tsigaridas. Symmetric tensor decomposition. Linear Algebra and Applications, 433:1851\u20131872, 2010.","journal-title":"Linear Algebra and Applications"},{"issue":"8","key":"9372_CR17","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","volume":"59","author":"Emmanuel J Cand\u00e8s","year":"2006","unstructured":"Emmanuel\u00a0J. Cand\u00e8s, Justin Romberg, and Terence Tao. Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics, 59(8):1207\u20131223, 2006.","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"9372_CR18","doi-asserted-by":"crossref","unstructured":"Constantin Carath\u00e9odory and Lip\u00f2t Fej\u00e9r. \u00dcber den Zusammenhang der Extremen von Harmonischen Funktionen mit Ihren Koeffizienten und \u00dcber den Picard-Landauschen Satz. In Rendiconti del Circolo Matematico di Palermo (1884-1940), volume\u00a032, pages 218\u2013239. 1911.","DOI":"10.1007\/BF03014796"},{"key":"9372_CR19","series-title":"Undergraduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2181-2","volume-title":"Ideals, Varieties, and Algorithms","author":"David A Cox","year":"1992","unstructured":"David\u00a0A. Cox, John Little, and Donal O\u2019Shea. Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics. Springer, 1992."},{"key":"9372_CR20","volume-title":"Solution of the Truncated Complex Moment Problem for Flat Data","author":"Raul\u00a0E Curto","year":"1996","unstructured":"Raul\u00a0E. Curto and Lawrence\u00a0A. Fialkow. Solution of the Truncated Complex Moment Problem for Flat Data. Amer Mathematical Society, Providence, R.I, January 1996."},{"issue":"1\u20132","key":"9372_CR21","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0377-0427(99)00028-X","volume":"105","author":"Annie Cuyt","year":"1999","unstructured":"Annie Cuyt. How well can the concept of Pad\u00e9 approximant be generalized to the multivariate case? Journal of Computational and Applied Mathematics, 105(1-2):25\u201350, 1999.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"9372_CR22","first-page":"24","volume":"1","author":"Baron Gaspard Riche de\u00a0Prony","year":"1795","unstructured":"Baron Gaspard\u00a0Riche de\u00a0Prony. Essai exp\u00e9rimental et analytique: sur les lois de la dilatabilit\u00e9 de fluides \u00e9lastiques et sur celles de la force expansive de la vapeur de l\u2019alcool, \u00e0 diff\u00e9rentes temp\u00e9ratures. J. \u00c9cole Polytechnique, 1:24\u201376, 1795.","journal-title":"J. \u00c9cole Polytechnique"},{"key":"9372_CR23","volume-title":"Commutative Algebra: With a View toward Algebraic Geometry, Graduate Texts in Mathematics","author":"David Eisunbud","year":"1994","unstructured":"David Eisunbud. Commutative Algebra: With a View toward Algebraic Geometry, volume 150 of Graduate Texts in Mathematics. Springer-Verlag, 1994."},{"key":"9372_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71647-1","volume-title":"Introduction \u00e0 la r\u00e9solution des syst\u00e8mes polynomiaux, Math\u00e9matiques & Applications","author":"Mohamed Elkadi","year":"2007","unstructured":"Mohamed Elkadi and Bernard Mourrain. Introduction \u00e0 la r\u00e9solution des syst\u00e8mes polynomiaux, volume\u00a059 of Math\u00e9matiques & Applications. Springer, Berlin, 2007."},{"key":"9372_CR25","first-page":"399","volume":"106","author":"Jacques Emsalem","year":"1978","unstructured":"Jacques Emsalem. G\u00e9om\u00e9trie des points \u00e9pais. Bulletin de la S.M.F., 106:399\u2013416, 1978.","journal-title":"Bulletin de la S.M.F."},{"issue":"1","key":"9372_CR26","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1007\/BF03014797","volume":"32","author":"Ernst Fischer","year":"1911","unstructured":"Ernst Fischer. \u00dcber das Carath\u00e9odory\u2019sche Problem, Potenzreihen mit positivem reellen Teil betreffend. Rendiconti del Circolo Matematico di Palermo (1884-1940), 32(1):240\u2013256, 1911.","journal-title":"Rendiconti del Circolo Matematico di Palermo (1884\u20131940)"},{"issue":"6","key":"9372_CR27","doi-asserted-by":"crossref","first-page":"1480","DOI":"10.1109\/18.59953","volume":"36","author":"Patrick Fitzpatrick","year":"1990","unstructured":"Patrick Fitzpatrick and Graham\u00a0H. Norton. Finding a basis for the characteristic ideal of an n-dimensional linear recurring sequence. IEEE Transactions on Information Theory, 36(6):1480\u20131487, 1990.","journal-title":"IEEE Transactions on Information Theory"},{"key":"9372_CR28","first-page":"231","volume":"94","author":"Michel Fliess","year":"1970","unstructured":"Michel Fliess. S\u00e9ries reconnaissables, rationnelles et alg\u00e9briques. Bulletin des Sciences Math\u00e9matiques. Deuxi\u00e8me S\u00e9rie, 94:231\u2013239, 1970.","journal-title":"Bulletin des Sciences Math\u00e9matiques. Deuxi\u00e8me S\u00e9rie"},{"issue":"8","key":"9372_CR29","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1016\/j.jsc.2008.11.003","volume":"44","author":"Mark Giesbrecht","year":"2009","unstructured":"Mark Giesbrecht, George Labahn, and Wen-shin Lee. Symbolic-numeric sparse interpolation of multivariate polynomials. J. Symb. Comput., 44(8):943\u2013959, August 2009.","journal-title":"J. Symb. Comput."},{"issue":"2","key":"9372_CR30","doi-asserted-by":"crossref","first-page":"R1","DOI":"10.1088\/0266-5611\/19\/2\/201","volume":"19","author":"Gene Golub","year":"2003","unstructured":"Gene Golub and Victor Pereyra. Separable nonlinear least squares: The variable projection method and its applications. Inverse Problems, 19(2):R1\u2013R26, 2003.","journal-title":"Inverse Problems"},{"key":"9372_CR31","unstructured":"N.\u00a0E. Golyandina and K.\u00a0D. Usevich. 2D-Extension of Singular Spectrum Analysis: Algorithm and Elements of Theory. In Matrix Methods: Theory, Algorithms and Applications, pages 449\u2013473. World Scientific Publishing, 2010."},{"key":"9372_CR32","doi-asserted-by":"crossref","unstructured":"Stef Graillat and Philippe Tr\u00e9buchet. A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system. In Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, pages 167\u2013174. ACM, 2009.","DOI":"10.1145\/1576702.1576727"},{"key":"9372_CR33","doi-asserted-by":"crossref","unstructured":"Wolfgang Gr\u00f6bner. \u00dcber das Macaulaysche inverse System und dessen Bedeutung f\u00fcr die Theorie der linearen Differentialgleichungen mit konstanten Koeffizienten. In Abhandlungen Aus Dem Mathematischen Seminar Der Universit\u00e4t Hamburg, volume 12, Issue 1, pages 127\u2013132. Springer, 1937.","DOI":"10.1007\/BF02948939"},{"key":"9372_CR34","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/S0024-3795(98)10223-9","volume":"288","author":"Gu Caixing","year":"1999","unstructured":"Caixing Gu. Finite rank Hankel operators on the polydisk. Linear Algebra and its Applications, 288:269\u2013281, 1999.","journal-title":"Linear Algebra and its Applications"},{"key":"9372_CR35","first-page":"89","volume":"10","author":"Hakop A Hakopian","year":"2004","unstructured":"Hakop\u00a0A. Hakopian and Mariam\u00a0G. Tonoyan. Partial differential analogs of ordinary differential equations and systems. New York J. Math, 10:89\u2013116, 2004.","journal-title":"New York J. Math"},{"key":"9372_CR36","volume-title":"An Introduction to Complex Analysis in Several Variables","author":"Lars Hormander","year":"1990","unstructured":"Lars Hormander. An Introduction to Complex Analysis in Several Variables, volume\u00a07. North Holland, Amsterdam; New York; N.Y., U.S.A., 3rd edition, 1990.","edition":"3"},{"key":"9372_CR37","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0093426","volume-title":"Power Sums, Gorenstein Algebras, and Determinantal Loci","author":"Anthony Iarrobino","year":"1999","unstructured":"Anthony Iarrobino and Vassil Kanev. Power Sums, Gorenstein Algebras, and Determinantal Loci. Lecture Notes in Mathematics. Springer, 1999."},{"key":"9372_CR38","unstructured":"Leopold Kronecker. Zur Theorie der Elimination Einer Variabeln aus Zwei Algebraischen Gleichungen. pages 535\u2013600, 1880."},{"key":"9372_CR39","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.laa.2015.10.023","volume":"490","author":"Stefan Kunis","year":"2016","unstructured":"Stefan Kunis, Thomas Peter, Tim R\u00f6mer, and Ulrich von der Ohe. A multivariate generalization of Prony\u2019s method. Linear Algebra and its Applications, 490:31\u201347, February 2016.","journal-title":"Linear Algebra and its Applications"},{"key":"9372_CR40","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.jsc.2012.03.007","volume":"51","author":"Jean-Bernard Lasserre","year":"2013","unstructured":"Jean-Bernard Lasserre, Monique Laurent, Bernard Mourrain, Philipp Rostalski, and Philippe Tr\u00e9buchet. Moment matrices, border bases and real radical computation. Journal of Symbolic Computation, 51:63\u201385, 2013.","journal-title":"Journal of Symbolic Computation"},{"key":"9372_CR41","doi-asserted-by":"crossref","unstructured":"Monique Laurent. Sums of squares, moment matrices and optimization over polynomials. In Emerging Applications of Algebraic Geometry, IMA Volumes in Mathematics and Its Applications, volume 149, pages 157\u2013270. Springer, New York, 2009.","DOI":"10.1007\/978-0-387-09686-5_7"},{"issue":"1","key":"9372_CR42","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s00013-009-0007-6","volume":"93","author":"Monique Laurent","year":"2009","unstructured":"Monique Laurent and Bernard Mourrain. A generalized flat extension theorem for moment matrices. Archiv der Mathematik, 93(1):87\u201398, 2009.","journal-title":"Archiv der Mathematik"},{"issue":"2","key":"9372_CR43","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1109\/TIT.2013.2291876","volume":"60","author":"Lek-Heng Lim","year":"2014","unstructured":"Lek-Heng Lim and Pierre Comon. Blind multilinear identification. IEEE Transactions on Information Theory, 60(2):1260\u20131280, 2014.","journal-title":"IEEE Transactions on Information Theory"},{"key":"9372_CR44","doi-asserted-by":"crossref","unstructured":"Francis S. Macaulay. The Algebraic Theory of Modular Systems. Cambridge University Press, 1916.","DOI":"10.3792\/chmm\/1263317740"},{"key":"9372_CR45","volume-title":"The Theory of Error-Correcting Codes, Volume 16","author":"Jessie\u00a0F MacWilliams","year":"1977","unstructured":"Jessie\u00a0F. MacWilliams and Neil J.\u00a0A. Sloane. The Theory of Error-Correcting Codes, Volume 16. North Holland Publishing Co., 1977."},{"key":"9372_CR46","doi-asserted-by":"crossref","first-page":"271","DOI":"10.5802\/aif.65","volume":"6","author":"Bernard Malgrange","year":"1956","unstructured":"Bernard Malgrange. Existence et approximation des solutions des \u00e9quations aux d\u00e9riv\u00e9es partielles et des \u00e9quations de convolution. Annales de l\u2019institut Fourier, 6:271\u2013355, 1956.","journal-title":"Annales de l\u2019institut Fourier"},{"issue":"1","key":"9372_CR47","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/TIT.1969.1054260","volume":"15","author":"James Massey","year":"1969","unstructured":"James Massey. Shift-register synthesis and BCH decoding. IEEE transactions on Information Theory, 15(1):122\u2013127, 1969.","journal-title":"IEEE transactions on Information Theory"},{"key":"9372_CR48","first-page":"469","volume":"117&118","author":"Bernard Mourrain","year":"1996","unstructured":"Bernard Mourrain. Isolated points, duality and residues. J. of Pure and Applied Algebra, 117&118:469\u2013493, 1996.","journal-title":"J. of Pure and Applied Algebra"},{"key":"9372_CR49","doi-asserted-by":"crossref","unstructured":"Bernard Mourrain. A new criterion for normal form algorithms. In M.\u00a0Fossorier, H.\u00a0Imai, Shu Lin, and A.\u00a0Poli, editors, Proc. AAECC, volume 1719 of LNCS, pages 430\u2013443. Springer, Berlin, 1999.","DOI":"10.1007\/3-540-46796-3_41"},{"issue":"1","key":"9372_CR50","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1006\/jcom.1999.0530","volume":"16","author":"Bernard Mourrain","year":"2000","unstructured":"Bernard Mourrain and Victor\u00a0Y. Pan. Multivariate Polynomials, Duality, and Structured Matrices. Journal of Complexity, 16(1):110\u2013180, 2000.","journal-title":"Journal of Complexity"},{"key":"9372_CR51","doi-asserted-by":"crossref","unstructured":"Bernard Mourrain and Philippe Tr\u00e9buchet. Generalized normal forms and polynomials system solving. In M.\u00a0Kauers, editor, Proc. of the International Symposium on Symbolic and Algebraic Computation (ISSAC\u201905), pages 253\u2013260, 2005.","DOI":"10.1145\/1073884.1073920"},{"issue":"3\u20134","key":"9372_CR52","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1023\/A:1011901522520","volume":"12","author":"Ulrich Oberst","year":"2001","unstructured":"Ulrich Oberst and Franz Pauer. The Constructive Solution of Linear Systems of Partial Difference and Differential Equations with Constant Coefficients. Multidimensional Systems and Signal Processing, 12(3-4):253\u2013308, 2001.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"1","key":"9372_CR53","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1006\/aima.1998.1782","volume":"141","author":"Paul S Pedersen","year":"1999","unstructured":"Paul\u00a0S. Pedersen. Basis for Power Series Solutions to Systems of Linear, Constant Coefficient Partial Differential Equations. Advances in Mathematics, 141(1):155\u2013166, 1999.","journal-title":"Advances in Mathematics"},{"key":"9372_CR54","first-page":"65","volume":"33","author":"Vladimir\u00a0V Peller","year":"1998","unstructured":"Vladimir\u00a0V. Peller. An excursion into the theory of Hankel operators. Holomorphic spaces (Berkeley, CA, 1995), Math. Sci. Res. Inst. Publ, 33:65\u2013120, 1998.","journal-title":"Holomorphic spaces (Berkeley, CA, 1995), Math. Sci. Res. Inst. Publ"},{"key":"9372_CR55","doi-asserted-by":"crossref","unstructured":"Victor\u00a0Pereyra and Godela\u00a0Scherer, editors. Exponential Data Fitting and Its Applications. Bentham Science Publisher, 2012.","DOI":"10.2174\/97816080504821100101"},{"issue":"2","key":"9372_CR56","doi-asserted-by":"crossref","first-page":"025001","DOI":"10.1088\/0266-5611\/29\/2\/025001","volume":"29","author":"Thomas Peter","year":"2013","unstructured":"Thomas Peter and Gerlind Plonka. A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators. Inverse Problems, 29(2):025001, 2013.","journal-title":"Inverse Problems"},{"issue":"2","key":"9372_CR57","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1002\/gamm.201410011","volume":"37","author":"Gerlind Plonka","year":"2014","unstructured":"Gerlind Plonka and Manfred Tasche. Prony methods for recovery of structured functions. GAMM-Mitteilungen, 37(2):239\u2013258, 2014.","journal-title":"GAMM-Mitteilungen"},{"issue":"5","key":"9372_CR58","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1016\/j.sigpro.2009.11.012","volume":"90","author":"Daniel Potts","year":"2010","unstructured":"Daniel Potts and Manfred Tasche. Parameter estimation for exponential sums by approximate prony method. Signal Processing, 90(5):1631\u20131642, 2010.","journal-title":"Signal Processing"},{"key":"9372_CR59","first-page":"204","volume":"40","author":"Daniel Potts","year":"2013","unstructured":"Daniel Potts and Manfred Tasche. Parameter estimation for multivariate exponential sums. Electronic Transactions on Numerical Analysis, 40:204\u2013224, 2013.","journal-title":"Electronic Transactions on Numerical Analysis"},{"key":"9372_CR60","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0024-3795(82)90110-0","volume":"48","author":"Stephen C Power","year":"1982","unstructured":"Stephen\u00a0C. Power. Finite rank multivariable Hankel forms. Linear Algebra and its Applications, 48:237\u2013244, 1982.","journal-title":"Linear Algebra and its Applications"},{"key":"9372_CR61","volume-title":"Les syst\u00e8mes d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles","author":"Charles Riquier","year":"1910","unstructured":"Charles Riquier. Les syst\u00e8mes d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles, volume XXVII. Gauthier-Villars, 1910."},{"issue":"2","key":"9372_CR62","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF01199078","volume":"10","author":"Richard Rochberg","year":"1987","unstructured":"Richard Rochberg. Toeplitz and Hankel operators on the Paley\u2013Wiener space. Integral Equations and Operator Theory, 10(2):187\u2013235, 1987.","journal-title":"Integral Equations and Operator Theory"},{"key":"9372_CR63","doi-asserted-by":"crossref","unstructured":"Richard Roy and Thomas Kailath. ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(7):984\u2013995, 1989.","DOI":"10.1109\/29.32276"},{"issue":"3","key":"9372_CR64","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S0747-7171(88)80033-6","volume":"5","author":"Shojiro Sakata","year":"1988","unstructured":"Shojiro Sakata. Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array. Journal of Symbolic Computation, 5(3):321\u2013337, 1988.","journal-title":"Journal of Symbolic Computation"},{"issue":"2","key":"9372_CR65","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/s00211-016-0844-8","volume":"136","author":"Tomas Sauer","year":"2017","unstructured":"Tomas Sauer. Prony\u2019s method in several variables. Numerische Mathematik, 136(2):411\u2013438, 2017.","journal-title":"Numerische Mathematik"},{"key":"9372_CR66","volume-title":"Th\u00e9orie des distributions","author":"Laurent Schwartz","year":"1966","unstructured":"Laurent Schwartz. Th\u00e9orie des distributions. Editions Hermann, Paris, 1966."},{"key":"9372_CR67","doi-asserted-by":"crossref","first-page":"1758","DOI":"10.1109\/78.143447","volume":"40","author":"The MUSIC Algorithm","year":"1992","unstructured":"A.\u00a0Lee Swindlehurst and Thomas Kailath. A Performance Analysis of Subspace-Based Methods in the Presence of Model Errors \u2013 Part I: The MUSIC Algorithm. IEEE Trans. on Signal Processing, 40:1758\u20131774, 1992.","journal-title":"IEEE Trans. on Signal Processing"},{"key":"9372_CR68","unstructured":"James\u00a0Joseph Sylvester. Essay on Canonical Form. The collected mathematical papers of J. J. Sylvester, Vol. I, Paper 34, Cambridge University Press. 1909 (XV und 688). G. Bell, London, 1851."},{"key":"9372_CR69","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139856065","volume-title":"Modern Computer Algebra","author":"Joachim von\u00a0zur Gathen","year":"2013","unstructured":"Joachim von\u00a0zur Gathen and J\u00fcrgen Gerhard. Modern Computer Algebra. Cambridge University Press, 3rd edition, 2013.","edition":"3"},{"issue":"6","key":"9372_CR70","doi-asserted-by":"crossref","first-page":"3685","DOI":"10.1109\/TIT.2016.2553041","volume":"62","author":"Zai Yang","year":"2016","unstructured":"Zai Yang, Lihua Xie, and Petre Stoica. Vandermonde Decomposition of Multilevel Toeplitz Matrices With Application to Multidimensional Super-Resolution. IEEE Transactions on Information Theory, 62(6):3685\u20133701, June 2016.","journal-title":"IEEE Transactions on Information Theory"},{"key":"9372_CR71","doi-asserted-by":"crossref","unstructured":"Richard Zippel. Probabilistic algorithms for sparse polynomials. In Proceedings of the International Symposiumon on Symbolic and Algebraic Computation, EUROSAM \u201979, pages 216\u2013226, London, UK, 1979. Springer-Verlag.","DOI":"10.1007\/3-540-09519-5_73"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-017-9372-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-017-9372-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-017-9372-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T18:53:16Z","timestamp":1659725596000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-017-9372-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,27]]},"references-count":71,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["9372"],"URL":"https:\/\/doi.org\/10.1007\/s10208-017-9372-x","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,27]]}}}