Recently, a characterization of frames in twisted shift-invariant spaces in L2(R2n) has been obtained in [16]. Using this result,we prove a sampling theorem on a subspace of a twisted shift-invariant space in this paper. © 2017 Walter de Gruyter GmbH, Berlin/Boston.

R Radha

Department of Mathematics

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IIT Madras

Advances in Pure and Applied Mathematics

In this paper, twisted shift-invariant spaces in L2(ℝ2n) are introduced. Characterizations of orthonormal system and Bessel sequence of twisted translates in L2(ℝ2n) are obtained in terms of Weyl transform. These results appear to be totally different from the classical case of characterizations of orthonormal systems and Bessel sequences of translates in L2(ℝn). Further, characterizations of frames, Riesz basis in twisted shift-invariant spaces in L2(ℝ2n)are also obtained. © 2015 Elsevier Inc.

Journal of Mathematical Analysis and Applications

Frames and Riesz bases of twisted shift-invariant spaces in L2(ℝ2n)

We study the theory of shift invariant spaces in L2(G), where G is a compact group. We define a range function and show that a relation between an H-invariant space and the range function is valid as in the case of abelian group setting. Here H is assumed to be a closed normal subgroup of G. We also obtain a decomposition for an H-invariant space in terms of principle H-invariant spaces whose generators give rise to "generalized Parseval frames" and use this result to study H-preserving operators. © 2012 Elsevier Masson SAS.

Journal	Data powered by TypesetAdvances in Pure and Applied Mathematics
Publisher	Data powered by TypesetWalter de Gruyter GmbH
ISSN	18671152
Open Access	No