Información General

• Autores: Sheldon Axler (coord.), John McCarthy (coord.), Donald Sarason (coord.)
• Editores: Cambridge University Press
• Año de publicación: 1998
• Colecciones: Mathematical Sciences Research Institute publications, 33
• País: Estados Unidos
• Idioma: inglés
• ISBN: 0-521-63193-9
• Texto completo no disponible (Saber más ...)

Resumen

• The term "Holomorphic Spaces" is short for "Spaces of Holomorphic Functions". It refers not so much to a branch of mathematics as to a common thread running through much of modern analysis---through functional analysis, operator theory, harmonic analysis, and, of course, complex analysis. In the fall of 1995 the Mathematical Sciences Research Institute in Berkeley sponsored the program Holomorphic Spaces. Over forty participants came for periods of two weeks to a full semester; an additional forty or so attended a week-long workshop in October. Spaces of holomorphic functions arise in many contexts. The MSRI program focused predominantely on operator-theoretic aspects of the subject. A series of minicourses formed the program's center- piece. This volume consists of expository articles by participants in the program (plus collaborators, in two cases), including several articles based on minicourses. The opening article, by Donald Sarason, gives an overview of several aspects of the subject. The remaining articles, while more special- ized, are nevertheless designed in varying degrees to be accessible to the nonexpert. A range of topics is addressed: Bergman spaces (Hakan Hedenmalm, Karl Stroethoff); Hankel operators in various guises (Vladimir Peller, Pamela Gorkin, Scott Saccone, Richard Rochberg); the Dirichlet space (Zhijian Wu); subnormal operators (John B. Conway and Liming Yang); operator models and related areas, especially interpolation problems and systems theory (Nikolai Nikolski and Vasily Vasyunin, Cora Sadosky, Nicholas Young, Alexander Kheifets, Harry Dym, James Rovnyak and coauthors). The concluding article, by Victor Vinnikov, describes an approach to certain commuting families of nonself-adjoint operators in which operator theory is linked with algebraic geometry.

Otros catálogos

• Red de Bibliotecas Universitarias (REBIUN)

Listado de artículos

• • Holomorphic Spaces: a Brief and Selective Survey

    Donald Sarason

    págs. 1-34

    

  • Recent Progress in the Function Theory of the Bergman Space

    Haakan Hedenmalm

    págs. 35-50

    

  • Harmonic Bergman Spaces

    Karel Stroethoff

    págs. 51-64

    

  • An Excursion into the Theory of Hankel Operators

    Vladimir V. Peller

    págs. 65-120

    

  • Hankel-Type Operators, Bourgain Algebras, and Uniform Algebras

    Pamela Gorkin

    págs. 121-134

    

  • Tight Uniform Algebras

    Scott Saccone

    págs. 135-154

    

  • Higher-Order Hankel Forms and Commutators

    Richard Rochberg

    págs. 155-178

    

  • Function Theory and Operator Theory on the Dirichlet Space

    Zhijian Wu

    págs. 179-200

    

  • Some Open Problems in the Theory of Subnormal Operators

    John Conway, Liming Yang

    págs. 201-210

    

  • Elements of Spectral Theory in Terms of the Free Function Model, Part I: basic Constructions

    Nikolai Nikolski, Vasily Vasyunin

    págs. 211-302

    

  • Liftings of Kernels Shift-Invariant in Scattering Systems

    Cora Sadosky

    págs. 303-336

    

  • Some Function-Theoretic Issues in Feedback Stabilisation

    Nicholas Young

    págs. 337-350

    

  • The Abstract Interpolation Problem and Applications

    Alexander Kheifets

    págs. 350-380

    

  • A Basic Interpolation Problem

    Harry Dym

    págs. 381-424

    

  • Reproducing Kernel Pontryagin Spaces

    Daniel Alpay, Aad Dijksma, James Rovnyak, Henk S. V. de Snoo

    págs. 425-444

    

  • Commuting Operators and Function Theory on a Riemann Surface

    Victor Vinnikov

    págs. 445-476