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On WH-packets of matrix-valued wave packet frames in $L^{2} (ℝ^{d}, ℂ^{s \times r})$

Jyoti

Department of Mathematics, University of Delhi, Delhi 110007, India

E-mail Address: jyoti.sheoran3@gmail.com

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and

Lalit K. Vashisht

Department of Mathematics, University of Delhi, Delhi 110007, India

E-mail Address: lalitkvashisht@gmail.com

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https://doi.org/10.1142/S0219691318500224Cited by:9 (Source: Crossref)

Abstract

A WH-packet is a system of vectors which is analogous to Aldroubi’s model for explicit expression of vectors (including frame vectors) in terms of a series associated with a given frame. In this paper, we study frame properties of WH-packet type system for matrix-valued wave packet frames in the function space $L^{2} (ℝ^{d}, ℂ^{s \times r})$ . A necessary and sufficient condition for WH-packets of matrix-valued wave packet frames in terms of a bounded below operator is given. We present sufficient conditions for both lower and upper frame conditions on scalars associated with WH-packet of matrix-valued wave packet frames. Finally, a Paley–Wiener type perturbation theorem for WH-packet of matrix-valued wave packet frames is given. Several examples are given to illustrate the results.

Keywords:

AMSC: 42C15, 42C30, 42C40

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