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Banach space aspects of frame theory with applications /

This book offers a fresh introduction to frame theory in Banach and Hilbert spaces, with a particular focus on the Banach space aspects of the frame theory and its applications. It presents some main developments from recent decades in the theory of frames, dilations, operator-valued measures, sampl...

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Bibliographic Details
Main Author: Han, Deguang
Other Authors: Hu, Qianfeng, Liu, Bei, Liu, Rui
Format: eBook
Language:English
Published: Cham : Springer Nature Switzerland : Imprint: Springer, 2026.
Edition:1st ed. 2026.
Series:Synthesis lectures on mathematics & statistics (Springer (Firm)),
Subjects:
Frames (Vector analysis)
Banach spaces.
Functional analysis.
Harmonic analysis.
Mathematical analysis.
Mathematics > Data processing.
Quantum computers.
Geometry, Differential.
Functional Analysis.
Abstract Harmonic Analysis.
Analysis.
Computational Mathematics and Numerical Analysis.
Quantum Computing.
Differential Geometry.
Analyse fonctionnelle.
Analyse harmonique.
Analyse mathématique.
Mathématiques > Informatique.
Ordinateurs quantiques.
Géométrie différentielle.
Electronic books.
Description
Summary:This book offers a fresh introduction to frame theory in Banach and Hilbert spaces, with a particular focus on the Banach space aspects of the frame theory and its applications. It presents some main developments from recent decades in the theory of frames, dilations, operator-valued measures, sampling, and related applications. By bridging topics from Banach space geometry, applied harmonic analysis, and quantum information theory, the authors highlight a novel perspective: frame theory not only serves as a powerful and central tool in mathematics and engineering, but is also deeply intertwined with the structure and theory of Banach spaces. Rather than providing an exhaustive treatment, the book aims to offer a broadly relevant and accessible overview that enables researchers across various fields to quickly grasp the foundational ideas and explore related research directions. In addition, this book: Blends functional analytic aspects of frames in Banach and Hilbert spaces with approximation properties, dilation theory, operator-valued measure, etc. Focuses on frames for Banach spaces and the intersection of Banach space geometry, even operator space structures Presents wide applications of frames in globally popular problems in quantum information theory and applied harmonic analysis, such as phase retrieval and quantum detection.
Physical Description:1 online resource (xiii, 270 pages) : illustrations.
ISBN:9783032101747 (electronic bk.)
3032101743
ISSN:1938-1751