{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:52Z","timestamp":1740123952054,"version":"3.37.3"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T00:00:00Z","timestamp":1716163200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T00:00:00Z","timestamp":1716163200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12071437"],"award-info":[{"award-number":["12071437"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Science and Technology Development Fund of Macau SAR","award":["FDCT0128\/2022\/A, 0020\/2023\/RIB1, 0111\/2023\/AFJ, 005\/2022\/ALC"],"award-info":[{"award-number":["FDCT0128\/2022\/A, 0020\/2023\/RIB1, 0111\/2023\/AFJ, 005\/2022\/ALC"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12271042"],"award-info":[{"award-number":["12271042"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s10444-024-10127-6","type":"journal-article","created":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T09:01:51Z","timestamp":1716195711000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A sparse approximation for fractional Fourier transform"],"prefix":"10.1007","volume":"50","author":[{"given":"Fang","family":"Yang","sequence":"first","affiliation":[]},{"given":"Jiecheng","family":"Chen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8780-9958","authenticated-orcid":false,"given":"Tao","family":"Qian","sequence":"additional","affiliation":[]},{"given":"Jiman","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,20]]},"reference":[{"issue":"11","key":"10127_CR1","doi-asserted-by":"publisher","first-page":"3084","DOI":"10.1109\/78.330368","volume":"42","author":"L Almeida","year":"1994","unstructured":"Almeida, L.: The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process 42(11), 3084\u20133091 (1994)","journal-title":"IEEE Trans. Signal Process"},{"key":"10127_CR2","unstructured":"Cartan, H.: Calcul differentiel, Hermann (1967)"},{"issue":"2","key":"10127_CR3","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1016\/j.jfa.2007.09.015","volume":"254","author":"E Cordero","year":"2008","unstructured":"Cordero, E., Nicola, F.: Metaplectic representation on Wiener amalgam spaces and applications to the Schr$$\\ddot{\\rm o}$$dinger equation. J. Funct. Anal. 254(2), 506\u2013534 (2008)","journal-title":"J. Funct. Anal."},{"issue":"2","key":"10127_CR4","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1112\/jlms\/jdt020","volume":"88","author":"E Cordero","year":"2013","unstructured":"Cordero, E., Tabacco, A., Wahlberg, P.: Schr$$\\ddot{\\rm o}$$dinger-type propagators, pseudodifferential operators and modulation spaces. J. Lond. Math. Soc. 88(2), 375\u2013395 (2013)","journal-title":"J. Lond. Math. Soc."},{"key":"10127_CR5","doi-asserted-by":"publisher","first-page":"778","DOI":"10.1007\/s00041-016-9489-3","volume":"23","author":"R Coifman","year":"2017","unstructured":"Coifman, R., Steinerberger, S.: Nonlinear phase unwinding of functions. J. Fourier Anal. Appl. 23, 778\u2013809 (2017)","journal-title":"J. Fourier Anal. Appl."},{"key":"10127_CR6","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1007\/s00041-018-9623-5","volume":"25","author":"R Coifman","year":"2019","unstructured":"Coifman, R., Peyriere, J.: Phase unwinding, or invariant subspace decompositions of Hardy spaces. J. Fourier Anal. Appl. 25, 684\u2013695 (2019)","journal-title":"J. Fourier Anal. Appl."},{"key":"10127_CR7","unstructured":"Duren, P.L.: Theory of $$H^p$$ spaces. Pure Appl. Math. 38, (2013)"},{"key":"10127_CR8","volume-title":"Quantum mechanics and path integrals","author":"RP Feynman","year":"1965","unstructured":"Feynman, R.P., Hibbs, A.R.: Quantum mechanics and path integrals. McGraw-Hill, New York (1965)"},{"key":"10127_CR9","unstructured":"Fu, Z.W., Hou, X.M., Wu, Q. Y.: Convergence of fractional Fourier series on the torus and applications (2022)"},{"issue":"7","key":"10127_CR10","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1119\/1.18910","volume":"66","author":"BR Holstein","year":"1998","unstructured":"Holstein, B.R.: The harmonic oscillator propagator. Am. J. Phys. 66(7), 583\u2013583 (1998)","journal-title":"Am. J. Phys."},{"key":"10127_CR11","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1016\/0022-247X(88)90094-7","volume":"136","author":"FH Kerr","year":"1988","unstructured":"Kerr, F.H.: Namias\u2019 fractional Fourier transforms on $$ L^2 $$ and applications to differential equations. J. Math. Anal. Appl. 136, 404\u2013418 (1988)","journal-title":"J. Math. Anal. Appl."},{"issue":"15","key":"10127_CR12","first-page":"675","volume":"247","author":"KI Kou","year":"2014","unstructured":"Kou, K.I., Morais, J.: Asymptotic behaviour of the quaternion linear canonical transform and the Bochner-Minlos theorem. Appl. Math. Comput. 247(15), 675\u2013688 (2014)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"10127_CR13","first-page":"196","volume":"55","author":"RM Lopez","year":"2009","unstructured":"Lopez, R.M., Suslov, S.K.: The Cauchy problem for a forced harmonic oscillator. Revista Mexicana De Fisica E 55(2), 196\u2013215 (2009)","journal-title":"Revista Mexicana De Fisica E"},{"issue":"6","key":"10127_CR14","doi-asserted-by":"publisher","first-page":"1370","DOI":"10.1016\/j.sigpro.2010.09.003","volume":"91","author":"X Li","year":"2011","unstructured":"Li, X., Bi, G., Stankovic, S., et al.: Local polynomial Fourier transform: a review on recent developments and applications. Signal Process. 91(6), 1370\u20131393 (2011)","journal-title":"Signal Process."},{"key":"10127_CR15","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1093\/imamat\/39.2.159","volume":"39","author":"AC McBride","year":"1987","unstructured":"McBride, A.C., Kerr, F.H.: On Namias\u2019s fractional Fourier transforms. IMA J. Appl. Math. 39, 159\u2013175 (1987)","journal-title":"IMA J. Appl. Math."},{"issue":"6","key":"10127_CR16","doi-asserted-by":"publisher","first-page":"1154","DOI":"10.1016\/j.automatica.2012.03.002","volume":"48","author":"W Mi","year":"2012","unstructured":"Mi, W., Qian, T.: Frequency-domain identification: an algorithm based on an adaptive rational orthogonal system. Automatica 48(6), 1154\u20131162 (2012)","journal-title":"Automatica"},{"issue":"1","key":"10127_CR17","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/j.sysconle.2011.10.016","volume":"61","author":"W Mi","year":"2012","unstructured":"Mi, W., Qian, T., Wan, F.: A fast adaptive model reduction method based on Takenaka-Malmquist systems. Syst. Control Lett. 61(1), 223\u2013230 (2012)","journal-title":"Syst. Control Lett."},{"issue":"4","key":"10127_CR18","doi-asserted-by":"publisher","first-page":"1550030","DOI":"10.1142\/S0219691315500307","volume":"13","author":"Y Mo","year":"2015","unstructured":"Mo, Y., Qian, T., Mi, W.: Sparse Representation in Szego kernels through reproducing kernel Hilbert space theory with applications. Int. J. Wavelet Multiresolut. Inf. Process. 13(4), 1550030 (2015)","journal-title":"Int. J. Wavelet Multiresolut. Inf. Process."},{"key":"10127_CR19","doi-asserted-by":"crossref","unstructured":"Mai, W., Shao, G.: On the Bergman kernel in weighted monogenic Bargmann-Fock spaces. Adv. Math. 415, (2023)","DOI":"10.1016\/j.aim.2023.108891"},{"key":"10127_CR20","doi-asserted-by":"crossref","unstructured":"Nikolski, N.: Hardy spaces, Cambridge University Press, (2019)","DOI":"10.1017\/9781316882108"},{"key":"10127_CR21","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1093\/imamat\/25.3.241","volume":"25","author":"V Namias","year":"1980","unstructured":"Namias, V.: The fractional order Fourier transform and its application to quantum mechanics. IMA J. Appl. Math. 25, 241\u2013265 (1980)","journal-title":"IMA J. Appl. Math."},{"key":"10127_CR22","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1002\/mma.1214","volume":"33","author":"T Qian","year":"2010","unstructured":"Qian, T.: Intrinsic mono-component decomposition of functions: an advance of Fourier theory. Math. Methods Appl. Sci. 33, 880\u2013891 (2010)","journal-title":"Math. Methods Appl. Sci."},{"issue":"8","key":"10127_CR23","doi-asserted-by":"publisher","first-page":"4210","DOI":"10.1002\/mma.8033","volume":"45","author":"T Qian","year":"2022","unstructured":"Qian, T.: Sparse representations of random signals. Math. Methods Appl. Sci. 45(8), 4210\u20134230 (2022)","journal-title":"Math. Methods Appl. Sci."},{"issue":"1","key":"10127_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S0219691313500070","volume":"11","author":"T Qian","year":"2013","unstructured":"Qian, T., Wang, Y.B.: Remarks on adaptive Fourier decomposition. Int. J. Wavelets Multiresolution Inf. Process. 11(1), 1\u201314 (2013)","journal-title":"Int. J. Wavelets Multiresolution Inf. Process."},{"issue":"6","key":"10127_CR25","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1080\/17476933.2013.787532","volume":"59","author":"T Qian","year":"2014","unstructured":"Qian, T., Chen, Q., Tan, L.: Rational orthogonal systems are Schauder bases. Complex Var. Elliptic Equ. 59(6), 841\u2013846 (2014)","journal-title":"Complex Var. Elliptic Equ."},{"issue":"10","key":"10127_CR26","doi-asserted-by":"publisher","first-page":"2431","DOI":"10.1002\/mma.3649","volume":"39","author":"T Qian","year":"2016","unstructured":"Qian, T.: Two-dimensional adaptive Fourier decomposition. Math. Methods Appl. Sci. 39(10), 2431\u20132448 (2016)","journal-title":"Math. Methods Appl. Sci."},{"issue":"3","key":"10127_CR27","first-page":"321","volume":"47","author":"T Qian","year":"2018","unstructured":"Qian, T.: A novel Fourier theory on non-linear phase and applications. Adv. Math. (China) 47(3), 321\u2013347 (2018)","journal-title":"Adv. Math. (China)"},{"issue":"1","key":"10127_CR28","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1002\/mma.1532","volume":"35","author":"T Qian","year":"2012","unstructured":"Qian, T., Sproessig, W., Wang, J.X.: Adaptive Fourier decomposition of functions in quaternionic Hardy spaces. Math. Methods Appl. Sci. 35(1), 43\u201364 (2012)","journal-title":"Math. Methods Appl. Sci."},{"issue":"3","key":"10127_CR29","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s10444-010-9153-4","volume":"34","author":"T Qian","year":"2011","unstructured":"Qian, T., Wang, Y.B.: Adaptive Fourier series-a variation of greedy algorithm. Adv. Comput. Math. 34(3), 279\u2013293 (2011)","journal-title":"Adv. Comput. Math."},{"issue":"2","key":"10127_CR30","first-page":"1","volume":"14","author":"T Qian","year":"2020","unstructured":"Qian, T.: Reproducing kernel sparse representations in relation to operator equations. Complex Anal. Oper. Theorem 14(2), 1\u201315 (2020)","journal-title":"Complex Anal. Oper. Theorem"},{"issue":"4","key":"10127_CR31","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1142\/S0219530521500251","volume":"20","author":"W Qu","year":"2021","unstructured":"Qu, W., Chui, C.K., Deng, G.T., Qian, T.: Sparse representation of approximation to identity. Anal. Appl. 20(4), 815\u2013837 (2021)","journal-title":"Anal. Appl."},{"issue":"4","key":"10127_CR32","doi-asserted-by":"publisher","first-page":"1827","DOI":"10.1007\/s11785-018-0862-x","volume":"13","author":"W Qu","year":"2019","unstructured":"Qu, W., Dang, P.: Rational approximation in a class of weighted Hardy spaces. Complex Anal. Oper. Theory 13(4), 1827\u20131852 (2019)","journal-title":"Complex Anal. Oper. Theory"},{"issue":"12","key":"10127_CR33","doi-asserted-by":"publisher","first-page":"4292","DOI":"10.1002\/mma.5648","volume":"42","author":"W Qu","year":"2019","unstructured":"Qu, W., Dang, P.: Reproducing kernel approximation in weighted Bergman spaces: algorithm and applications. Math. Methods Appl. Sci. 42(12), 4292\u20134304 (2019)","journal-title":"Math. Methods Appl. Sci."},{"key":"10127_CR34","unstructured":"Rudin, W.: Real and complex analysis 2nd. McGraw-Hill, (1974)"},{"key":"10127_CR35","volume-title":"Principles of mathematical analysis","author":"W Rudin","year":"1976","unstructured":"Rudin, W.: Principles of mathematical analysis. McGraw-hill, New York (1976)"},{"key":"10127_CR36","doi-asserted-by":"crossref","unstructured":"Saitoh, S., Sawano, Y.: Theory of reproducing kernels and applications. Developments in Mathematics 44, (2016)","DOI":"10.1007\/978-981-10-0530-5"},{"key":"10127_CR37","doi-asserted-by":"crossref","unstructured":"Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean space, Princeton University Press, (1971)","DOI":"10.1515\/9781400883899"},{"key":"10127_CR38","unstructured":"Toft, J., Bhimani, D., Manna, R.: Fractional Fourier transforms, powers of harmonic oscillators and their propagators on Pilipovic and modulation spaces (2021)"},{"issue":"2","key":"10127_CR39","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0165-1684(95)00107-7","volume":"47","author":"V Katkovnik","year":"1995","unstructured":"Katkovnik, V.: A new form of the Fourier transform for time-varying frequency estimation. Signal Process 47(2), 187\u2013200 (1995)","journal-title":"Signal Process"},{"key":"10127_CR40","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1002\/sapm19298170","volume":"8","author":"N Wiener","year":"1929","unstructured":"Wiener, N.: Hermitian polynomials and Fourier analysis. J. Math. Phys. 8, 70\u201373 (1929)","journal-title":"J. Math. Phys."},{"key":"10127_CR41","doi-asserted-by":"crossref","unstructured":"Yosida, B.: Functional analysis, Springer-Verlag, (1978)","DOI":"10.1007\/978-3-642-96439-8"},{"key":"10127_CR42","doi-asserted-by":"crossref","unstructured":"Yang, F., Chen, M., Li, P.T., Qu, W., Chen, J.C., Qian, T.: Sparse series solutions of random boundary and initial value problems, International Journal of Wavelets, Multiresolution and Information Processing (2023)","DOI":"10.1142\/S0219691323500509"},{"key":"10127_CR43","doi-asserted-by":"crossref","unstructured":"Zhu, K.: Analysis on Fock spaces, Springer Science and Business Media (2012)","DOI":"10.1007\/978-1-4419-8801-0"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-024-10127-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-024-10127-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-024-10127-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T12:17:23Z","timestamp":1719922643000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-024-10127-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,20]]},"references-count":43,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["10127"],"URL":"https:\/\/doi.org\/10.1007\/s10444-024-10127-6","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2024,5,20]]},"assertion":[{"value":"19 May 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 May 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"50"}}