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E-grāmata: Noncommutative Function-Theoretic Operator Theory and Applications

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, (College of William and Mary, Virginia)
  • Formāts: PDF+DRM
  • Sērija : Cambridge Tracts in Mathematics
  • Izdošanas datums: 16-Dec-2021
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781009020107
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Noncommutative Function-Theoretic Operator Theory and ApplicationsPalielināt
  • Formāts: PDF+DRM
  • Sērija : Cambridge Tracts in Mathematics
  • Izdošanas datums: 16-Dec-2021
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781009020107
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"This concise monograph explores how core ideas in Hardy -space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system -theory ideas and reproducing -kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling-Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspacesubspaces form a generalized orthogonal decomposition of the ambient Hardy space. Allthis leads to the de Branges-Rovnyak model theory and characteristic operator function for a Hilbert -space contraction operator. The chapters that follow generalize the system theory and reproducing -kernel techniques to enable an extension of the ideasabove to weighted Bergman -space multivariable settings"--

Recenzijas

'Noncommutative Function-Theoretic Operator Theory and Applications by Ball and Bolotnikov is a comprehensive monograph by acknowledged experts in the fields of operator theory and function theory. It gives an account of a very active area of modern research, to which the authors themselves have been major contributors. The significant themes of the book include reproducing kernel Hilbert spaces (notably weighted Bergman spaces), Beurling-Lax theorems, and systems-theoretic ideas expressed in operator-theoretic terms. The work as a whole is presented in a multivariable noncommutative context, and thus extends classical work on Hardy-space function theory and related operator theory.' Jonathan Partington, University of Leeds

Papildus informācija

This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.
Preface ix
Acknowledgments x
1 Introduction
1(25)
1.1 Function-Theoretic Operator Theory on Vectorial Hardy Spaces, Reproducing Kernel Hilbert Spaces, and Discrete-Time Linear Systems: Background
1(2)
1.2 The Synthesis of the Systems-Theory and Reproducing Kernel Approaches
3(8)
1.3 Standard Weighted Bergman Spaces
11(3)
1.4 The Hardy-Fock Space Setting
14(2)
1.5 Weighted Bergman-Fock Spaces
16(3)
1.6 Overview
19(6)
1.7 Notes
25(1)
2 Formal Reproducing Kernel Hilbert Spaces
26(16)
2.1 Basic Definitions
26(9)
2.2 Weighted Hardy-Fock Spaces
35(6)
2.3 Notes
41(1)
3 Contractive Multipliers
42(61)
3.1 Contractive Multipliers in General
43(6)
3.2 Contractive Multipliers between Hardy-Fock Spaces
49(23)
3.3 A Noncommutative Leech's Theorem
72(6)
3.4 Contractive Multipliers from Hu2(F+) to H2ω y(F+d) for Admissible ω
78(17)
3.5 Hω-y(F+d)-Bergman-Inner Formal Power Series
95(5)
3.6 Notes
100(3)
4 Stein Relations and Observability Range Spaces
103(77)
4.1 Preliminaries on Functional Calculus for the Operator BA
104(9)
4.2 Observability, Defect and Shifted Defect Operators
113(23)
4.3 Shifted Observability Operators and Observability Gramians
136(3)
4.4 The Model Shift-Operator Tuple on Hω y(F+d)
139(7)
4.5 A Wold Decomposition for ω-Isometric-like Operator Tuples
146(11)
4.6 Observability-Operator Range Spaces
157(11)
4.7 Notes
168(12)
5 Beurling-Lax Theorems Based on Contractive Multipliers
180(35)
5.1 Beurling-Lax Representations with Model Space H2u(F+d)
180(22)
5.2 Beurling-Lax Representations Based on Contractive Multipliers from Hω U(F+d) to Hω y(F+d)
202(3)
5.3 Representations with Model Space of the Form +nj=1 Aj.Uj (F+d)
205(7)
5.4 Notes
212(3)
6 Non-orthogonal Beurling-Lax Representations Based on Wandering Subspaces
215(15)
6.1 Beurling-Lax Quasi-Wandering Subspace Representations
216(5)
6.2 Non-orthogonal Beurling-Lax Representations Based on Wandering Subspaces
221(8)
6.3 Notes
229(1)
7 Orthogonal Beurling-Lax Representations Based on Wandering Subspaces
230(55)
7.1 Transfer Functions OωUβ and Metric Constraints
230(12)
7.2 Beurling-Lax Representations Based on Bergman-Inner Families
242(23)
7.3 Expansive Multiplier Property
265(13)
7.4 Bergman-Inner Multipliers as Extremal Solutions of Interpolation Problems
278(6)
7.5 Notes
284(1)
8 Models for ω-Hypercontractive Operator Tuples
285(30)
8.1 Model Theory Based on Observability Operators
286(5)
8.2 The Characteristic Function Approach
291(18)
8.3 Model Theory for n-Hypercontractions
309(4)
8.4 Notes
313(2)
9 Weighted Hardy-Fock Spaces Built from a Regular Formal Power Series
315(100)
9.1 Preliminaries
315(7)
9.2 The Spaces - H2ωp, n, Y(F+d) and Their Contractive Multipliers
322(32)
9.3 Output Stability, Stein Equations, and Inequalities
354(13)
9.4 The ωp,n-Shift Model Operator Tuple Sωp,n, R
367(3)
9.5 Observability Operator Range Spaces in H2ωp,n Y(F+d)
370(2)
9.6 Beurling-Lax Theorems Based on Contractive Multipliers
372(11)
9.7 Beurling-Lax Representations via Quasi-Wandering Subspaces
383(2)
9.8 Beurling-Lax Representations Based on Bergman-Inner Families
385(14)
9.9 Operator Model Theory for c.n.c. *-(p,n)-Hypercontractive Tuples
399(12)
9.10 Notes
411(4)
References 415(10)
Notation Index 425(2)
Subject Index 427
Joseph A. Ball is Professor Emeritus at Virginia Tech in Blacksburg, Virginia. He won Virginia Tech's Alumni Award for Research Excellence in 1997 and is a member of the 2019 class of Fellows of the American Mathematical Society. He is co-author of Interpolation of Rational Matrix Functions (1990). Vladimir Bolotnikov is Professor of Mathematics at William & Mary in Williamsburg, Virginia. He has published over a hundred papers in operator and function theory.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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