Approximation of the Inverse Frame Operator and Stability of Hilbert–Schmidt Frames

Anirudha Poria

doi:10.1007/s00009-017-0956-0

Approximation of the Inverse Frame Operator and Stability of Hilbert–Schmidt Frames

Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

Indian Institute of Technology Guwahati

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

14 Citations (Scopus)

Abstract

In this paper, we study the Hilbert–Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how the inverse of the HS-frame operator can be approximated using finite-dimensional methods. Finally, we present a classical perturbation result and prove that HS-frames are stable under small perturbations.

Original language	English
Article number	153
Journal	Mediterranean Journal of Mathematics
Volume	14
Issue number	4
DOIs	https://doi.org/10.1007/s00009-017-0956-0
Publication status	Published - 1 Aug 2017

Keywords

Frames
Hilbert–Schmidt frames
HS-Riesz bases
Inverse HS-frame operator
Perturbation
Projection method
Stability

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abstract = "In this paper, we study the Hilbert–Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how the inverse of the HS-frame operator can be approximated using finite-dimensional methods. Finally, we present a classical perturbation result and prove that HS-frames are stable under small perturbations.",

keywords = "Frames, Hilbert–Schmidt frames, HS-Riesz bases, Inverse HS-frame operator, Perturbation, Projection method, Stability",

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AB - In this paper, we study the Hilbert–Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how the inverse of the HS-frame operator can be approximated using finite-dimensional methods. Finally, we present a classical perturbation result and prove that HS-frames are stable under small perturbations.

KW - Frames

KW - Hilbert–Schmidt frames

KW - HS-Riesz bases

KW - Inverse HS-frame operator

KW - Perturbation

KW - Projection method

KW - Stability

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JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 4

M1 - 153

ER -

Approximation of the Inverse Frame Operator and Stability of Hilbert–Schmidt Frames

Abstract

Keywords

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