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Introduction to Model Spaces and their Operators [Kõva köide]

(Pomona College, California), (Université Laval, Québec), (University of Richmond, Virginia)
  • Formaat: Hardback, 340 pages, kõrgus x laius x paksus: 235x157x23 mm, kaal: 600 g, Worked examples or Exercises; 4 Halftones, unspecified; 6 Line drawings, unspecified
  • Sari: Cambridge Studies in Advanced Mathematics
  • Ilmumisaeg: 17-May-2016
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1107108748
  • ISBN-13: 9781107108745
Teised raamatud teemal:
Introduction to Model Spaces and their OperatorsSuurem pilt
  • Formaat: Hardback, 340 pages, kõrgus x laius x paksus: 235x157x23 mm, kaal: 600 g, Worked examples or Exercises; 4 Halftones, unspecified; 6 Line drawings, unspecified
  • Sari: Cambridge Studies in Advanced Mathematics
  • Ilmumisaeg: 17-May-2016
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1107108748
  • ISBN-13: 9781107108745
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781107108745.html
Märksõnad:
The study of model spaces is a broad field with connections to complex analysis, operator theory, engineering and mathematical physics. This self-contained text is the ideal introduction for newcomers, quickly taking them through the history of the subject and then pointing towards areas of future research.

The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

Muu info

A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.
Preface xi
Notation xiv
1 Preliminaries
1(31)
1.1 Measure and integral
1(7)
1.2 Poisson integrals
8(14)
1.3 Hilbert spaces and their operators
22(9)
1.4 Notes
31(1)
2 Inner functions
32(26)
2.1 Disk automorphisms
32(1)
2.2 Bounded analytic functions
33(3)
2.3 Inner functions
36(6)
2.4 Unimodular boundary limits
42(4)
2.5 Angular derivatives
46(6)
2.6 Frostman's Theorem
52(3)
2.7 Notes
55(3)
3 Hardy spaces
58(25)
3.1 Three approaches to the Hardy space
58(8)
3.2 The Riesz projection
66(1)
3.3 Factorization
67(6)
3.4 A growth estimate
73(1)
3.5 Associated classes of functions
74(4)
3.6 Notes
78(3)
3.7 For further exploration
81(2)
4 Operators on the Hardy space
83(21)
4.1 The shift operator
83(7)
4.2 Toeplitz operators
90(3)
4.3 A characterization of Toeplitz operators
93(3)
4.4 The commutant of the shift
96(3)
4.5 The backward shift
99(1)
4.6 Difference quotient operator
100(2)
4.7 Notes
102(1)
4.8 For further exploration
102(2)
5 Model spaces
104(22)
5.1 Model spaces as invariant subspaces
104(2)
5.2 Stability under conjugate analytic Toeplitz operators
106(2)
5.3 Containment and lattice operations
108(1)
5.4 A decomposition for Ku
109(2)
5.5 Reproducing kernels
111(1)
5.6 The projection Pu
112(3)
5.7 Finite-dimensional model spaces
115(3)
5.8 Density results
118(2)
5.9 Takenaka-Malmquist-Walsh bases
120(1)
5.10 Notes
121(3)
5.11 For further exploration
124(2)
6 Operators between model spaces
126(18)
6.1 Littlewood Subordination Principle
126(3)
6.2 Composition operators on model spaces
129(5)
6.3 Unitary maps between model spaces
134(3)
6.4 Multipliers of Ku
137(2)
6.5 Multipliers between two model spaces
139(2)
6.6 Notes
141(1)
6.7 For further exploration
142(2)
7 Boundary behavior
144(26)
7.1 Pseudocontinuation
144(7)
7.2 Cyclicity via pseudocontinuation
151(1)
7.3 Analytic continuation
152(6)
7.4 Boundary limits
158(9)
7.5 Notes
167(3)
8 Conjugation
170(17)
8.1 Abstract conjugations
170(3)
8.2 Conjugation on Ku
173(4)
8.3 Inner functions in Ku
177(1)
8.4 Generators of Ku
178(2)
8.5 Cartesian decomposition
180(2)
8.6 2 x 2 inner functions
182(3)
8.7 Notes
185(2)
9 The compressed shift
187(28)
9.1 What is a compression?
187(2)
9.2 The compressed shift
189(4)
9.3 Invariant subspaces and cyclic vectors
193(2)
9.4 The Sz.-Nagy-Foias model
195(2)
9.5 Functional calculus for Su
197(4)
9.6 The spectrum of Su
201(5)
9.7 The C*-algebra generated by Su
206(6)
9.8 Notes
212(1)
9.9 For further exploration
213(2)
10 The commutant lifting theorem
215(16)
10.1 Minimal isometric dilations
216(1)
10.2 Existence and uniqueness
217(5)
10.3 Strong convergence
222(1)
10.4 An associated partial isometry
223(1)
10.5 The commutant lifting theorem
224(5)
10.6 The characterization of {SUY}'
229(1)
10.7 Notes
230(1)
11 Clark measures
231(29)
11.1 The family of Clark measures
231(4)
11.2 The Clark unitary operators
235(4)
11.3 Spectral representation of the Clark operator
239(6)
11.4 The Aleksandrov disintegration theorem
245(2)
11.5 A connection to composition operators
247(3)
11.6 Carleson measures
250(1)
11.7 Isometric embeddings
251(5)
11.8 Notes
256(2)
11.9 For further exploration
258(2)
12 Riesz bases
260(22)
12.1 Minimal sequences
260(3)
12.2 Uniformly minimal sequences
263(2)
12.3 Uniformly separated sequences
265(3)
12.4 The mappings A, V, and Γ
268(3)
12.5 Abstract Riesz sequences
271(5)
12.6 Riesz sequences in KB
276(1)
12.7 Completeness problems
277(1)
12.8 Notes
278(4)
13 Truncated Toeplitz operators
282(25)
13.1 The basics
282(5)
13.2 A characterization
287(4)
13.3 C-symmetric operators
291(1)
13.4 The spectrum of Auψ
292(7)
13.5 An operator disintegration formula
299(1)
13.6 Norm of a truncated Toeplitz operator
300(1)
13.7 Notes
301(4)
13.8 For further exploration
305(2)
References 307(11)
Index 318
Stephan Ramon Garcia is an Associate Professor at Pomona College, California. He has earned multiple NSF research grants and five teaching awards from three different institutions. He has also authored over 50 research articles in operator theory, complex analysis, matrix analysis, and number theory. Javad Mashreghi is a Professor of Mathematics at Université Laval, Québec, where he has been selected Star Professor of the Year seven times for excellence in teaching. His main fields of interest are complex analysis, operator theory and harmonic analysis. He is the author of several mathematical textbooks, monographs and research articles. He won the G. de B. Robinson Award, the publication prize of the Canadian Mathematical Society, in 2004. William T. Ross is the Roger Francis and Mary Saunders Richardson Chair in Mathematics at the University of Richmond, Virginia. He is the author of over 40 research papers in function theory and operator theory and also four books.