SEMI-CONTINUOUS G-FRAMES IN HILBERT SPACES

Anirudha Poria

doi:10.31392/MFAT-npu263.2020.06

SEMI-CONTINUOUS G-FRAMES IN HILBERT SPACES

Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

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

1 Citation (Scopus)

Abstract

In this paper, we introduce the concept of semi-continuous g-frames in Hilbert spaces. We first construct an example of semi-continuous g-frames using the Fourier transform of the Heisenberg group and study the structure of such frames. Then, as an application we provide some fundamental identities and inequalities for semi-continuous g-frames. Finally, we present a classical perturbation result and prove that semi-continuous g-frames are stable under small perturbations.

Original language	English
Pages (from-to)	249-261
Number of pages	13
Journal	Methods of Functional Analysis and Topology
Volume	26
Issue number	3
DOIs	https://doi.org/10.31392/MFAT-npu263.2020.06
Publication status	Published - 2020

Keywords

continuous g-frames
frame identity
g-frames
perturbation
semi-continuous g-frames
stability

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10.31392/MFAT-npu263.2020.06

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title = "SEMI-CONTINUOUS G-FRAMES IN HILBERT SPACES",

abstract = "In this paper, we introduce the concept of semi-continuous g-frames in Hilbert spaces. We first construct an example of semi-continuous g-frames using the Fourier transform of the Heisenberg group and study the structure of such frames. Then, as an application we provide some fundamental identities and inequalities for semi-continuous g-frames. Finally, we present a classical perturbation result and prove that semi-continuous g-frames are stable under small perturbations.",

keywords = "continuous g-frames, frame identity, g-frames, perturbation, semi-continuous g-frames, stability",

author = "Anirudha Poria",

note = "Funding Information: The author is deeply indebted to Dr. Azita Mayeli for several valuable comments and suggestions. The author is grateful to the United States-India Educational Foundation for providing the Fulbright-Nehru Doctoral Research Fellowship, and Department of Mathematics and Computer Science, the Graduate Center, City University of New York, New York, USA for its kind hospitality during the period of this work. He would also like to express his gratitude to the Norbert Wiener Center for Harmonic Analysis and Applications at the University of Maryland, College Park for its kind support. Publisher Copyright: {\textcopyright} 2020. All Rights Reserved.",

year = "2020",

doi = "10.31392/MFAT-npu263.2020.06",

language = "English",

volume = "26",

pages = "249--261",

journal = "Methods of Functional Analysis and Topology",

issn = "1029-3531",

number = "3",

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T1 - SEMI-CONTINUOUS G-FRAMES IN HILBERT SPACES

AU - Poria, Anirudha

N1 - Funding Information: The author is deeply indebted to Dr. Azita Mayeli for several valuable comments and suggestions. The author is grateful to the United States-India Educational Foundation for providing the Fulbright-Nehru Doctoral Research Fellowship, and Department of Mathematics and Computer Science, the Graduate Center, City University of New York, New York, USA for its kind hospitality during the period of this work. He would also like to express his gratitude to the Norbert Wiener Center for Harmonic Analysis and Applications at the University of Maryland, College Park for its kind support. Publisher Copyright: © 2020. All Rights Reserved.

PY - 2020

Y1 - 2020

N2 - In this paper, we introduce the concept of semi-continuous g-frames in Hilbert spaces. We first construct an example of semi-continuous g-frames using the Fourier transform of the Heisenberg group and study the structure of such frames. Then, as an application we provide some fundamental identities and inequalities for semi-continuous g-frames. Finally, we present a classical perturbation result and prove that semi-continuous g-frames are stable under small perturbations.

AB - In this paper, we introduce the concept of semi-continuous g-frames in Hilbert spaces. We first construct an example of semi-continuous g-frames using the Fourier transform of the Heisenberg group and study the structure of such frames. Then, as an application we provide some fundamental identities and inequalities for semi-continuous g-frames. Finally, we present a classical perturbation result and prove that semi-continuous g-frames are stable under small perturbations.

KW - continuous g-frames

KW - frame identity

KW - g-frames

KW - perturbation

KW - semi-continuous g-frames

KW - stability

UR - https://www.scopus.com/pages/publications/85097412970

U2 - 10.31392/MFAT-npu263.2020.06

DO - 10.31392/MFAT-npu263.2020.06

M3 - Article

AN - SCOPUS:85097412970

SN - 1029-3531

VL - 26

SP - 249

EP - 261

JO - Methods of Functional Analysis and Topology

JF - Methods of Functional Analysis and Topology

IS - 3

ER -

SEMI-CONTINUOUS G-FRAMES IN HILBERT SPACES

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Keywords

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