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...

Full description

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:

MARC

Tag First Indicator Second Indicator Subfields
LEADER 00000cam a2200000 i 4500
001 in00005778980
005 20260418233626.0
006 m o d
007 cr cnu||||||||
008 260216s2026 sz a o 000 0 eng d
040 |a SFB  |b eng  |e rda  |e pn  |c SFB  |d OCLCO  |d UKKRT  |d YDX  |d EBLCP  |d OCLCQ  |d GW5XE 
019 |a 1573525050  |a 1573768913 
020 |a 9783032101747 (electronic bk.) 
020 |a 3032101743 
020 |z 3032101735 
020 |z 9783032101730 
024 7 |a 10.1007/978-3-032-10174-7  |2 doi 
035 |a (OCoLC)1577567539  |z (OCoLC)1573525050  |z (OCoLC)1573768913 
050 4 |a QA433  |b .H35 2026 
072 7 |a PBKF  |2 bicssc 
072 7 |a MAT037000  |2 bisacsh 
072 7 |a PBKF  |2 thema 
082 0 4 |a 515.7  |2 23 
100 1 |a Han, Deguang. 
245 1 0 |a Banach space aspects of frame theory with applications /  |c by Deguang Han, Qianfeng Hu, Bei Liu, Rui Liu. 
250 |a 1st ed. 2026. 
264 1 |a Cham :  |b Springer Nature Switzerland :  |b Imprint: Springer,  |c 2026. 
300 |a 1 online resource (xiii, 270 pages) :  |b illustrations. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
341 0 |b PDF/UA-1  |2 onix 
341 0 |b No reading system accessibility options actively disabled  |2 onix 
341 0 |b Table of contents navigation  |2 onix 
341 0 |b Single logical reading order  |2 onix 
341 0 |b Short alternative textual descriptions  |2 onix 
341 0 |b Use of color is not sole means of conveying information  |2 onix 
341 0 |b Use of high contrast between text and background color  |2 onix 
341 0 |b Next / Previous structural navigation  |2 onix 
341 0 |b All non-decorative content supports reading without sight  |2 onix 
490 1 |a Synthesis Lectures on Mathematics & Statistics,  |x 1938-1751 
505 0 |a Frames in Hilbert Spaces -- Frames in Banach Spaces -- Approximation Properties -- Banach Dilation -- Nonselfadjoint Dilation and Generalized Choi-Kraus Representation -- Quantum Detection and Phase Retrieval. 
520 |a 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. 
532 8 |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com 
650 0 |a Frames (Vector analysis) 
650 0 |a Banach spaces. 
650 0 |a Functional analysis. 
650 0 |a Harmonic analysis. 
650 0 |a Mathematical analysis. 
650 0 |a Mathematics  |x Data processing. 
650 0 |a Quantum computers. 
650 0 |a Geometry, Differential. 
650 1 4 |a Functional Analysis. 
650 2 4 |a Abstract Harmonic Analysis. 
650 2 4 |a Analysis. 
650 2 4 |a Computational Mathematics and Numerical Analysis. 
650 2 4 |a Quantum Computing. 
650 2 4 |a Differential Geometry. 
650 6 |a Analyse fonctionnelle. 
650 6 |a Analyse harmonique. 
650 6 |a Analyse mathématique. 
650 6 |a Mathématiques  |x Informatique. 
650 6 |a Ordinateurs quantiques. 
650 6 |a Géométrie différentielle. 
655 0 |a Electronic books. 
700 1 |a Hu, Qianfeng. 
700 1 |a Liu, Bei. 
700 1 |a Liu, Rui. 
776 0 8 |z 3032101735 
776 0 8 |c Original  |z 3032101735  |z 9783032101730  |w (OCoLC)1541765094 
830 0 |a Synthesis lectures on mathematics & statistics (Springer (Firm)),  |x 1938-1751 
852 8 |b POD  |z This title is available for the library to purchase for your use. Click the "Purchase It For Me" button to place a request. This item will take 5-10 business days to arrive. 
955 |a Ebook POD title 
961 |m 565731 
999 f f |i 06d57a57-4ed5-4e23-ade7-1d3736922998  |s 449f1a49-dddc-4ba5-a969-cfa278fbcc59  |t 0 
952 f f |a Texas A&M University  |b College Station  |c Sterling C. Evans Library  |s Evans POD  |d Purchase on Demand  |t 0  |e QA433 .H35 2026  |h Library of Congress classification 
998 f f |a QA433 .H35 2026  |t 0  |l Purchase on Demand