Positive Weight Function and Classification of g-Frames

Anirudha Poria

doi:10.1080/01630563.2020.1728771

Positive Weight Function and Classification of g-Frames

Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Given a positive weight function and an isometry map on a Hilbert spaces (Formula presented.) we study a class of linear maps which is a g-frame, g-Riesz basis, and a g-orthonormal basis for (Formula presented.) with respect to (Formula presented.) in terms of the weight function. We apply our results to study the frame for shift-invariant subspaces on the Heisenberg group.

Original language	English
Pages (from-to)	950-968
Number of pages	19
Journal	Numerical Functional Analysis and Optimization
Volume	41
Issue number	8
DOIs	https://doi.org/10.1080/01630563.2020.1728771
Publication status	Published - 10 Jun 2020

Keywords

g-frames
g-Riesz bases
Heisenberg group
shift-invariant subspaces
weight function

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10.1080/01630563.2020.1728771

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abstract = "Given a positive weight function and an isometry map on a Hilbert spaces (Formula presented.) we study a class of linear maps which is a g-frame, g-Riesz basis, and a g-orthonormal basis for (Formula presented.) with respect to (Formula presented.) in terms of the weight function. We apply our results to study the frame for shift-invariant subspaces on the Heisenberg group.",

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AB - Given a positive weight function and an isometry map on a Hilbert spaces (Formula presented.) we study a class of linear maps which is a g-frame, g-Riesz basis, and a g-orthonormal basis for (Formula presented.) with respect to (Formula presented.) in terms of the weight function. We apply our results to study the frame for shift-invariant subspaces on the Heisenberg group.

KW - g-frames

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KW - Heisenberg group

KW - shift-invariant subspaces

KW - weight function

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Positive Weight Function and Classification of g-Frames

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Keywords

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