Riesz sequences of translates and generalized duals with support on [0, 1] |
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| Authors: | O. Christensen H. O. Kim R. Y. Kim J. K. Lim |
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| Affiliation: | (1) Department of Mathematics, Technical University of Denmark, Building 303, 2800 Lyngby, Denmark;(2) Division of Applied Mathematics, KAIST, 373-1, Guseong-dong, Yuseong-gu, 305-701 Daejeon, Republic of Korea;(3) Department of Mathematics, Yeungnam University, 214-1, Dae-dong, Gyeongsan-si, 712-749 Gyeongsangbuk-do, Republic of Korea;(4) Department of Computational Mathematics and Informatics, Hankyong National University, 67 Sokjong-Dong, Ansung-City, 456-749 Kyonggi-Do, Republic of Korea |
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| Abstract: | If the integer translates of a function ø with compact support generate a frame for a subspace W of L 2(?),then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. Considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. Extending work by Ben-Artzi and Ron, we characterize the existence of oblique duals generated by a function with support on an interval of length one. If such a generator exists, we show that it can be chosen with desired smoothness. Regardless whether ø is polynomial or not, the same condition implies that a polynomial dual supported on an interval of length one exists. |
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| Keywords: | KeywordHeading" >Math Subject Classifications 42C15 |
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