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THEORY OF BERGMAN SPACES (GRADUATE TEXTS IN MATHEMATICS By Hakan Hedenmalm NEW
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eBay item number:226894367595
Item specifics
- Condition
- Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
- ISBN-10
- 0387987916
- Book Title
- Theory of Bergman Spaces (Graduate Texts in Mathematics (199))
- Genre
- Calculus & mathematical analysis
- ISBN
- 9780387987910
About this product
Product Identifiers
Publisher
Springer New York
ISBN-10
0387987916
ISBN-13
9780387987910
eBay Product ID (ePID)
1667890
Product Key Features
Number of Pages
IX, 289 Pages
Language
English
Publication Name
Theory of Bergman Spaces
Subject
Geometry / Algebraic, Mathematical Analysis
Publication Year
2000
Type
Textbook
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Height
0.3 in
Item Weight
46.9 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
99-053568
Dewey Edition
21
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 Number
199
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515
Table Of Content
1 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.
Synopsis
15 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 Number
QA299.6-433
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- 1***j (18)- Feedback left by buyer.Past monthVerified purchasePrompt delivery, product as advertised
- s***n (78)- Feedback left by buyer.Past monthVerified purchaseFrank Zappa with the wrecking crew, how can you go wrong ? This was a good deal, we had a little problem with the cd. However it was solved quickly. We came to an amicable decision. And I am happy ! I would recommend Zuber to my friends and family ! A good company to do business with ! 👍
- 1***e (776)- Feedback left by buyer.Past monthVerified purchaseExcellent seller! Highly recommended!