Let G be a second countable locally compact abelian group. The aim of this paper is to characterize the left translates on the Heisenberg group [Formula presented] to be frames and Riesz bases in terms of the group Fourier transform. © 2018 Royal Dutch Mathematical Society (KWG)

R Radha

Department of Mathematics

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IIT Madras

Indagationes Mathematicae

In this paper, it is shown that for a fixed m ∈ N, Z/m is a stable set of sampling for V(φ 1 , φ 2 , . . . , φ s ) if and only if there exists γ &gt; 0 such that | detΦ(x)| ≥ γ a.e. on T, where Φ is a symbol matrix of a block Laurent operator associated with the sample set of φ l , l = 1, . . . , s. A similar result is proved when rZ where r = p/q, p, q ∈ N and gcd(p, q) = 1,is a stable set of sampling for V(φ) (single generator) as well as V(φ 1 , φ 2 , . . . , φ s ) (multi generators). A perturbation of stable set of sampling is also discussed. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Applicable Analysis

Invertibility of Laurent operators and shift invariant spaces with finitely many generators

In this paper, we extend to the context of locally compact abelian groups, the notion of Weyl transform. We also define and characterize Weyl multipliers for certain function spaces. A dual space characterization is provided for the space of Weyl multipliers on Lp spaces. Finally we also study the twisted shift-invariant subspaces. © 2017, Springer International Publishing AG.

Journal of Pseudo-Differential Operators and Applications

Weyl transform and Weyl multipliers associated with locally compact abelian groups

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.

Fulltext

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 TypesetIndagationes Mathematicae
Publisher	Data powered by TypesetElsevier B.V.
ISSN	00193577
Open Access	Yes