{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T03:48:56Z","timestamp":1773373736023,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1993,2,1]],"date-time":"1993-02-01T00:00:00Z","timestamp":728524800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[1993,2]]},"DOI":"10.1007\/bf02070823","type":"journal-article","created":{"date-parts":[[2005,9,17]],"date-time":"2005-09-17T19:57:57Z","timestamp":1126987077000},"page":"109-126","source":"Crossref","is-referenced-by-count":11,"title":["Wavelet bases for a set of commuting unitary operators"],"prefix":"10.1007","volume":"1","author":[{"given":"T. N. T.","family":"Goodman","sequence":"first","affiliation":[]},{"given":"S. L.","family":"Lee","sequence":"additional","affiliation":[]},{"given":"W. S.","family":"Tang","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF02070823_CR1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1002\/cpa.3160440202","volume":"44","author":"G. Beylkin","year":"1991","unstructured":"G. Beylkin, R. Coifman and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math. 44(1991)141\u2013183.","journal-title":"Comm. Pure Appl. Math."},{"key":"BF02070823_CR2","doi-asserted-by":"crossref","unstructured":"C. de Boor, R. DeVore and A. Ron, On the construction of multivariate (pre) wavelets, CMS-TRS University of Wisconsin-Madison 92-9 (1992).","DOI":"10.21236\/ADA247105"},{"key":"BF02070823_CR3","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1090\/S0002-9939-1991-1077784-X","volume":"113","author":"K.C. Chui","year":"1991","unstructured":"K.C. Chui and J.-Z. Wang, A cardinal spline approach to wavelets, Proc. Amer. Math. Soc. 113(1991)785\u2013793.","journal-title":"Proc. Amer. Math. Soc."},{"key":"BF02070823_CR4","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1090\/S0002-9947-1992-1076613-3","volume":"330","author":"K.C. Chui","year":"1992","unstructured":"K.C. Chui and J.-Z. Wang, On compactly supported spline wavelets and a duality principle, Trans. Amer. Math. Soc. 330(1992)903\u2013915.","journal-title":"Trans. Amer. Math. Soc."},{"key":"BF02070823_CR5","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/BF02836340","volume":"8","author":"K.C. Chui","year":"1992","unstructured":"K.C. Chui, J. St\u00f6ckler and J.D. Ward, Compactly supported box-spline wavelets, Approx. Theory Appl. 8(1992)77\u2013100.","journal-title":"Approx. Theory Appl."},{"key":"BF02070823_CR6","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1002\/cpa.3160410705","volume":"41","author":"I. Daubechies","year":"1988","unstructured":"I. Daubechies, Orthonormal bases of compactly supported wavelet, Comm. Pure Appl. Math. 41(1988)909\u2013996.","journal-title":"Comm. Pure Appl. Math."},{"key":"BF02070823_CR7","doi-asserted-by":"crossref","unstructured":"T.N.T. Goodman, S.L. Lee and W.S. Tang, Wavelets in wandering subspaces, Trans. Amer. Math. Soc., to appear.","DOI":"10.1090\/S0002-9947-1993-1117215-0"},{"key":"BF02070823_CR8","unstructured":"T.N.T. Goodman and S.L. Lee, Wavelets of multiplicityr, Applied Analysis Report, AA\/921, February 1992, University of Dundee."},{"key":"BF02070823_CR9","doi-asserted-by":"crossref","unstructured":"P.R. Halmos,A Hilbert Space Problem Book, 2nd ed. (Springer, 1982).","DOI":"10.1007\/978-1-4684-9330-6"},{"key":"BF02070823_CR10","unstructured":"N. Jacobson,Basic Algebra (W.H. Freeman, 1973)."},{"key":"BF02070823_CR11","first-page":"95","volume":"68","author":"S. Jaffard","year":"1989","unstructured":"S. Jaffard and Y. Meyer, Bases d'ondelettes dans des ouverts de \u221d n , J. de Math. Pures et Appl. 68(1989)95\u2013108.","journal-title":"J. de Math. Pures et Appl."},{"key":"BF02070823_CR12","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/B978-0-12-438660-0.50036-4","volume-title":"Curves and Surfaces","author":"R.Q. Jia","year":"1991","unstructured":"R.Q. Jia and C.A. Micchelli, Using the refinement equation of the construction of pre-wavelets II: Powers of two, in:Curves and Surfaces, ed. P.J. Laurent, A. Le M\u00e9haut\u00e9 and L.L. Schumaker (Academic Press, New York, 1991) pp. 209\u2013246."},{"key":"BF02070823_CR13","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF02241706","volume":"48","author":"R.Q. Jia","year":"1992","unstructured":"R.Q. Jia and C.A. Micchelli, Using the refinement for the construction of pre-wavelets V: Extensibility of trigonometric polynomials, Computing 48(1992)61\u201372.","journal-title":"Computing"},{"key":"BF02070823_CR14","unstructured":"R.Q. Jia and Z.W. Shen, Multiresolution and wavelets, Preprint."},{"key":"BF02070823_CR15","unstructured":"S.L. Lee, H.H. Tan and W.S. Tang, Wavelet bases for a unitary operator, Preprint."},{"key":"BF02070823_CR16","first-page":"227","volume":"67","author":"P.G. Lemari\u00e9","year":"1988","unstructured":"P.G. Lemari\u00e9, Ondelettes \u00e1 localisation exponentielles, J. de Math. Pures et Appl. 67(1988)227\u2013236.","journal-title":"J. de Math. Pures et Appl."},{"key":"BF02070823_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4171\/RMI\/22","volume":"2","author":"P.G. Lemari\u00e9","year":"1986","unstructured":"P.G. Lemari\u00e9 and Y. Meyer, Ondelettes et bases hilbertiennes, Rev. Mat. Iberoamericana 2(1986)1\u201318.","journal-title":"Rev. Mat. Iberoamericana"},{"key":"BF02070823_CR18","first-page":"69","volume":"315","author":"S. Mallat","year":"1989","unstructured":"S. Mallat, Multiresolution approximations and wavelet orthonormal bases ofL 2(\u211d), Trans. Amer. Math. Soc. 315(1989)69\u201387.","journal-title":"Trans. Amer. Math. Soc."},{"key":"BF02070823_CR19","volume-title":"Ondelettes et fonctions splines, Seminaire Equations aux Deriv\u00e9es Partielles","author":"Y. Meyer","year":"1986","unstructured":"Y. Meyer, Ondelettes et fonctions splines, Seminaire Equations aux Deriv\u00e9es Partielles, Ecole Polytechnique, Paris (December 1986)."},{"key":"BF02070823_CR20","unstructured":"Y. Meyer, Principle d'incertitude, bases hilbertiennes et alg\u00e8bres d'op\u00e9rateurs, Bourbaki Seminar, No. 662 (1985\u201386)."},{"key":"BF02070823_CR21","doi-asserted-by":"crossref","unstructured":"C.A. Micchelli, Using the refinement equation for the construction of pre-wavelets VI: Shift-invariant subspaces, in:Proc. NATO ASI, Maratea, Italy (April 1991).","DOI":"10.1007\/978-94-011-2634-2_10"},{"key":"BF02070823_CR22","first-page":"133","volume-title":"Approximation Theory and Functional Analysis","author":"S. Riemenschneider","year":"1991","unstructured":"S. Riemenschneider and Z.W. Shen, Box spline, cardinal series, and wavelets, in:Approximation Theory and Functional Analysis, ed. C.K. Chui (Academic Press, New York, 1991) pp. 133\u2013149."},{"key":"BF02070823_CR23","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/0021-9045(92)90129-C","volume":"7","author":"S. Riemenschneider","year":"1992","unstructured":"S. Riemenschneider and Z.W. Shen, Wavelets and prewavelets in low dimensions, J. Approx. Theory 7(1992)18\u201338.","journal-title":"J. Approx. Theory"},{"key":"BF02070823_CR24","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1090\/S0002-9939-1965-0174977-5","volume":"16","author":"J.B. Robertson","year":"1965","unstructured":"J.B. Robertson, On wandering subspaces for unitary operators, Proc. Amer. Math. Soc. 16(1965)233\u2013236.","journal-title":"Proc. Amer. Math. Soc."},{"key":"BF02070823_CR25","volume-title":"Fourier Analysis on Groups","author":"W. Rudin","year":"1962","unstructured":"W. Rudin,Fourier Analysis on Groups (Interscience, New York, 1962)."},{"key":"BF02070823_CR26","series-title":"CBMS-NSF Series in Appl. Math.","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970555","volume-title":"Cardinal spline interpolation","author":"I.J. Schoenberg","year":"1973","unstructured":"I.J. Schoenberg, Cardinal spline interpolation, CBMS-NSF Series in Appl. Math. No. 12 (SIAM, Philadelphia, 1973)."},{"key":"BF02070823_CR27","unstructured":"R.M. Young,Introduction to Nonharmonic Fourier Series (Academic Press, 1980)."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02070823.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02070823\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02070823","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T01:04:20Z","timestamp":1706576660000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02070823"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,2]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,2]]}},"alternative-id":["BF02070823"],"URL":"https:\/\/doi.org\/10.1007\/bf02070823","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,2]]}}}