{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T15:51:09Z","timestamp":1726415469115},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multidim Syst Sign Process"],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1007\/s11045-014-0285-4","type":"journal-article","created":{"date-parts":[[2014,3,11]],"date-time":"2014-03-11T01:52:36Z","timestamp":1394502756000},"page":"439-457","source":"Crossref","is-referenced-by-count":6,"title":["Algorithms for the theory of restrictions of scalar $$n$$ n -D systems to proper subspaces of $$\\mathbb {R}^n$$ R n"],"prefix":"10.1007","volume":"26","author":[{"given":"Debasattam","family":"Pal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harish K.","family":"Pillai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"285_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-35651-8","volume-title":"Ideals, varieties, and algorithms: Undergraduate texts in mathematics","author":"D Cox","year":"2007","unstructured":"Cox, D., Little, J., & O\u2019Shea, D. (2007). Ideals, varieties, and algorithms: Undergraduate texts in mathematics (3rd ed.). Berlin: Springer.","edition":"3"},{"key":"285_CR2","volume-title":"Commutative algebra with a view toward algebraic geometry","author":"D Eisenbud","year":"1995","unstructured":"Eisenbud, D. (1995). Commutative algebra with a view toward algebraic geometry. Berlin: Springer."},{"issue":"6","key":"285_CR3","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1137\/0331070","volume":"31","author":"E Fornasini","year":"1993","unstructured":"Fornasini, E., Rocha, P., & Zampieri, S. (1993). State space realization of 2-D finite-dimensional behaviours. SIAM Journal on Control and Optimization, 31(6), 1502\u20131517.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"285_CR4","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s11045-010-0124-1","volume":"22","author":"C Kojima","year":"2010","unstructured":"Kojima, C., Rapisarda, P., & Takaba, K. (2010). Lyapunov stability analysis of higher order 2-D systems. Multidimensional Systems and Signal Processing, 22, 287\u2013302.","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"285_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-70628-1","volume-title":"Computational commutative algebra 2","author":"M Kreuzer","year":"2000","unstructured":"Kreuzer, M., & Robbiano, L. (2000). Computational commutative algebra 2. Berlin: Springer."},{"issue":"34","key":"285_CR6","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.sysconle.2010.01.005","volume":"59","author":"D Napp Avelli","year":"2010","unstructured":"Napp Avelli, D., & Rocha, P. (2010). Autonomous multidimensional systems and their implementation by behavioral control. Systems and Control Letters, 59(34), 203\u2013208.","journal-title":"Systems and Control Letters"},{"issue":"4","key":"285_CR7","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1080\/00207179.2011.575800","volume":"84","author":"D Napp Avelli","year":"2011","unstructured":"Napp Avelli, D., Rapisarda, P., & Rocha, P. (2011). Lyapunov stability of 2D finite-dimensional behaviours. International Journal of Control, 84(4), 737\u2013745.","journal-title":"International Journal of Control"},{"key":"285_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00046908","volume":"20","author":"U Oberst","year":"1990","unstructured":"Oberst, U. (1990). Multidimensional constant linear systems. Acta Applicandae Mathematicae, 20, 1\u2013175.","journal-title":"Acta Applicandae Mathematicae"},{"key":"285_CR9","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1023\/A:1011901522520","volume":"12","author":"U Oberst","year":"2001","unstructured":"Oberst, U., & Pauer, F. (2001). The constructive solution of linear systems of partial difference and differential equations with constant coefficients. Multidimensional Systems and Signal Processing, 12, 253\u2013308.","journal-title":"Multidimensional Systems and Signal Processing"},{"key":"285_CR10","first-page":"205","volume-title":"Constructive algebra and systems theory","author":"U Oberst","year":"2006","unstructured":"Oberst, U. (2006). The constructive solution of linear systems of partial difference and differential equations with constant coefficients. In B. Hanzon & M. Hazewinkel (Eds.), Constructive algebra and systems theory (pp. 205\u2013233). Amsterdam: Royal Netherlands Academy of Arts and Sciences."},{"key":"285_CR11","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s11045-012-0194-3","volume":"25","author":"D Pal","year":"2014","unstructured":"Pal, D., & Pillai, H. K. (2014). On restrictions of $$n$$ n -D systems to 1-D subspaces. Multidimensional Systems and Signal Processing, 25, 115\u2013144.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"5","key":"285_CR12","doi-asserted-by":"crossref","first-page":"1406","DOI":"10.1137\/S0363012900368028","volume":"40","author":"HK Pillai","year":"2002","unstructured":"Pillai, H. K., & Willems, J. C. (2002). Lossless and dissipative distributed systems. SIAM Journal on Control and Optimization, 40(5), 1406\u20131430.","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"1","key":"285_CR13","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s00013-004-1282-x","volume":"84","author":"W Plesken","year":"2005","unstructured":"Plesken, W., & Robertz, D. (2005). Janets approach to presentations and resolutions for polynomials and linear pdes. Archiv der Mathematik, 84(1), 22\u201337.","journal-title":"Archiv der Mathematik"},{"key":"285_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-2539-2","volume-title":"Partial differential equations and group theory: New perspectives for applications","author":"J-F Pommaret","year":"1994","unstructured":"Pommaret, J.-F. (1994). Partial differential equations and group theory: New perspectives for applications. Dordrecht: Kluwer."},{"key":"285_CR15","volume-title":"An introduction to partial differential equations","author":"M Renardy","year":"2004","unstructured":"Renardy, M., & Rogers, R. C. (2004). An introduction to partial differential equations. New York: Springer."},{"key":"285_CR16","volume-title":"Les Syst\u00e8mes d\u2019\u00c9quations aux D\u00e9riv\u00e9es Partielles","author":"C Riquier","year":"1910","unstructured":"Riquier, C. (1910). Les Syst\u00e8mes d\u2019\u00c9quations aux D\u00e9riv\u00e9es Partielles. Paris: Gauthiers-Villars."},{"key":"285_CR17","unstructured":"Rocha, P. (1990) Structure and representation of 2-D systems. PhD thesis, University of Groningen, The Netherlands"},{"key":"285_CR18","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1023\/A:1008434613435","volume":"11","author":"S Shankar","year":"2000","unstructured":"Shankar, S. (2000). Can one control the vibrations of a drum? Multidimensional Systems and Signal Processing, 11, 67\u201381.","journal-title":"Multidimensional Systems and Signal Processing"},{"issue":"3","key":"285_CR19","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1109\/81.841912","volume":"47","author":"ME Valcher","year":"2001","unstructured":"Valcher, M. E. (2001). Characteristic cones and stability properties of two-dimensional autonomous behaviors. IEEE Transactions on Circuits and Systems-Part I: Fundamental Theory and Applications, 47(3), 290\u2013302.","journal-title":"IEEE Transactions on Circuits and Systems-Part I: Fundamental Theory and Applications"},{"issue":"3","key":"285_CR20","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1109\/9.73561","volume":"36","author":"JC Willems","year":"1991","unstructured":"Willems, J. C. (1991). Paradigms and puzzles in the theory of dynamical systems. IEEE Transactions on Automatic Control, 36(3), 259\u2013294.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"285_CR21","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/BF02741885","volume":"11","author":"J Wood","year":"1998","unstructured":"Wood, J., Rogers, E., & Owens, D. H. (1998). A formal theory of matrix primeness. Mathematics of Control, Signals, and Systems, 11, 40\u201378.","journal-title":"Mathematics of Control, Signals, and Systems"},{"key":"285_CR22","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF00997120","volume":"31","author":"E Zerz","year":"1993","unstructured":"Zerz, E., & Oberst, U. (1993). The canonical cauchy problem for linear systems of partial difference equations with constant coefficients over the complete $$r$$ r -dimensional integral lattice $$\\mathbb{Z}^r$$ Z r . Acta Applicandae Mathematicae., 31, 249\u2013273.","journal-title":"Acta Applicandae Mathematicae."}],"container-title":["Multidimensional Systems and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-014-0285-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11045-014-0285-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11045-014-0285-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T23:44:01Z","timestamp":1559346241000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11045-014-0285-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,12]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["285"],"URL":"https:\/\/doi.org\/10.1007\/s11045-014-0285-4","relation":{},"ISSN":["0923-6082","1573-0824"],"issn-type":[{"value":"0923-6082","type":"print"},{"value":"1573-0824","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,12]]}}}