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**About this book :- **
**Holomorphic Spaces ** written by
** Sheldon Axler, John E. McCarthy, Donald Sarason **

Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists, and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by program participants describing the present state of the art. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.

(Sheldon Axler)

**Book Detail :- **
** Title: ** Holomorphic Spaces
** Edition: **
** Author(s): ** Sheldon Axler, John E. McCarthy, Donald Sarason
** Publisher: ** Cambridge University Press
** Series: ** Mathematical Sciences Research Institute Publications
** Year: ** 1998
** Pages: ** 445
** Type: ** PDF
** Language: ** English
** ISBN: ** 0521631939,9780521631938
** Country: ** US

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**About Author :- **

Author ** Sheldon Axler ** was valedictorian of his high school in Miami, Florida. He received his AB from Princeton University with highest honors, followed by a PhD in Mathematics from the University of California at Berkeley. As a Moore Instructor at MIT, Axler received a university-wide teaching award.

Axler was then an assistant professor, associate professor, and professor in the Mathematics Department at Michigan State University, where he received the first J. Sutherland Frame Teaching Award and the Distinguished Faculty Award.

Axler received the Lester R. Ford Award for expository writing from the Mathematical Association of America in 1996. In addition to publishing numerous research papers, Axler is the author of five mathematics textbooks, ranging from freshman to graduate level. His book Linear Algebra Done Right has been adopted as a textbook at over 260 universities.

Axler has served as Editor-in-Chief of the Mathematical Intelligencer and as Associate Editor of the American Mathematical Monthly. He has been a member of the Council of the American Mathematical Society and a member of the Board of Trustees of the Mathematical Sciences Research Institute. Axler currently serves on the editorial board of Springer’s series Undergraduate Texts in Mathematics, Graduate Texts in Mathematics, and Universitext.

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**Book Contents :- **
**Holomorphic Spaces ** written by
** Sheldon Axler, John E. McCarthy, Donald Sarason **
cover the following topics.

The Abstract Interpolation Problem and Applications by ALEXANDER KHEIFETS

Holomorphic Spaces: A Brief and Selective Survey by DONALD SARASON

Higher-Order Hankel Forms and Commutators by RICHARD ROCHBERG

Function Theory and Operator Theory on the Dirichlet Space by ZHIJIAN WU

Some Open Problems in the Theory of Subnormal Operators by JOHN B. CONWAY AND LIMING YANG

Recent Progress in the Function Theory of the Bergman Space by H°AKAN HEDENMALM

Elements of Spectral Theory in Terms of the Free Function Model Part I: Basic Constructions by NIKOLAI NIKOLSKI AND VASILY VASYUNIN

Liftings of Kernels Shift-Invariant in Scattering Systems by CORA SADOSKY

Some Function-Theoretic Issues in Feedback Stabilisation by NICHOLAS YOUNG

A Basic Interpolation Problem by HARRY DYM

Reproducing Kernel Pontryagin Spaces by DANIEL ALPAY, AAD DIJKSMA, JAMES ROVNYAK, AND HENDRIK S. V. DE SNOO

An Excursion into the Theory of Hankel Operators by VLADIMIR V. PELLER

Hankel-Type Operators, Bourgain Algebras, and Uniform Algebras by PAMELA GORKIN

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