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Graduate Texts in Mathematics Ser.: Theory of Bergman Spaces by Hakan Hedenmalm, Kehe Zhu and Boris Korenblum (2000, Hardcover)
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-100387987916
ISBN-139780387987910
eBay Product ID (ePID)1667890
Product Key Features
Number of PagesIX, 289 Pages
LanguageEnglish
Publication NameTheory of Bergman Spaces
SubjectGeometry / Algebraic, Mathematical Analysis
Publication Year2000
TypeTextbook
Subject AreaMathematics
AuthorHakan Hedenmalm, Kehe Zhu, Boris Korenblum
SeriesGraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.3 in
Item Weight46.9 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN99-053568
Dewey Edition21
Reviews"Each chapter ends with a section called Notes and another called Exercises and Further Results. ... It would be quite suitable for graduate students in the field." (Lou Zengjian, zbMATH 0955.32003, 2022)
Series Volume Number199
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515
Table Of Content1 The Bergman Spaces.- 1.1 Bergman Spaces.- 1.2 Some Lp Estimates.- 1.3 The Bloch Space.- 1.4 Duality of Bergman Spaces.- 1.5 Notes.- 1.6 Exercises and Further Results.- 2 The Berezin Transform.- 2.1 Algebraic Properties.- 2.2 Harmonic Functions.- 2.3 Carleson-Type Measures.- 2.4 BMO in the Bergman Metric.- 2.5 A Lipschitz Estimate.- 2.6 Notes.- 2.7 Exercises and Further Results.- 3 Ap -Inner Functions.- 3.1 Ap? -Inner Functions.- 3.2 An Extremal Problem.- 3.3 The Biharmonic Green function.- 3.4 The Expansive Multiplier Property.- 3.5 Contractive Zero Divisors in Ap.- 3.6 An Inner-Outer Factorization Theorem for Ap.- 3.7 Approximation of Subinner Functions.- 3.8 Notes.- 3.9 Exercises and Further Results.- 4 Zero Sets.- 4.1 Some Consequences of Jensen's Formula.- 4.2 Notions of Density.- 4.3 The Growth Spaces A-? and A-'.- 4.4 A-? Zero Sets, Necessary Conditions.- 4.5 A-? Zero Sets, a Sufficient Condition.- 4.6 Zero Sets for AP'.- 4.7 The Bergman-Nevanlinna Class.- 4.8 Notes.- 4.9 Exercises and Further Results.- 5 Interpolation and Sampling.- 5.1 Interpolation Sequences for AT-'.- 5.2 Sampling Sets for A-'.- 5.3 Interpolation and Sampling in Ap'.- 5.4 Hyperbolic Lattices.- 5.5 Notes.- 5.6 Exercises and Further Results.- 6 Invariant Subspaces.- 6.1 Invariant Subspaces of Higher Index.- 6.2 Inner Spaces in A2'.- 6.3 A Beurling-Type Theorem.- 6.4 Notes.- 6.5 Exercises and Further Results.- 7 Cyclicity.- 7.1 Cyclic Vectors as Outer functions.- 7.2 Cyclicity in Ap Versus in A-'.- 7.3 Premeasures for Functions in A-'.- 7.4 Cyclicity in A-'.- 7.5 Notes.- 7.6 Exercises and Further Results.- 8 Invertible Noncyclic Functions.- 8.1 An Estimate for Harmonic Functions.- 8.2 The Building Blocks.- 8.3 The Basic Iteration Scheme.- 8.4 The Mushroom Forest.- 8.5 Finishing the Construction.- 8.6 Two Applications.- 8.7 Notes.- 8.8 Exercises and Further Results.- 9 Logarithmically Subharmonic Weights.- 9.1 Reproducing Kernels.- 9.2 Green Functions with Smooth Weights.- 9.3 Green Functions with General Weights.- 9.4 An Application.- 9.5 Notes.- 9.6 Exercises and Further Results.- References.
Synopsis15 years ago the function theory and operator theory connected with the Hardy spaces was well understood. None of the techniques that led to all the information about Hardy spaces worked on their close relatives the Bergman spaces. Most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely. Now the situation has completely changed. Today there are rich theories describing the Bergman spaces and their operators. Research interest and research activity in the area has been high for several years. A book is badly needed on Bergman spaces., Preliminary Text. Do not use. 15 years ago the function theory and operator theory connected with the Hardy spaces was well understood (zeros; factorization; interpolation; invariant subspaces; Toeplitz and Hankel operators, etc.). None of the techniques that led to all the information about Hardy spaces worked on their close relatives the Bergman spaces. Most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely. Now the situation has completely changed. Today there are rich theories describing the Bergman spaces and their operators. Research interest and research activity in the area has been high for several years. A book is badly needed on Bergman spaces and the three authors are the right people to write it., Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research interest and activity have expanded in this area and there are now rich theories describing the Bergman spaces and their operators. This book is a timely treatment of the theory, written by three of the major players in the field.
LC Classification NumberQA299.6-433
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