Holomorphic Spaces

Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.

Sheldon Axler (Edited by), John E. McCarthy (Edited by), Donald Sarason (Edited by)

9780521101035, Cambridge University Press

Paperback / softback, published 5 February 2009

488 pages
23.4 x 15.6 x 2.5 cm, 0.68 kg

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 programme participants. 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.

Preface
1. Holomorphic spaces: a brief and selective survey Donald Sarason
2. Recent progress in the function theory of the Bergman space Håkan Hedenmalm
3. Harmonic Bergman spaces Karel Stroethoff
4. An excursion into the theory of Hankel operators Vladimir V. Peller
5. Hankel-type operators, Bourgain algebras and uniform algebras Pamela Gorkin
6. Tight uniform algebras Scott Saccone
7. Higher-order Hankel forms and commutators Richard Rochberg
8. Function theory and operator theory on the Dirichlet space Zhijian Wu
9. Some open problems in the theory of subnormal operators John B. Conway and Liming Yang
10. Elements of spectral theory in terms of the free function model part I: basic constructions Nikolai Nikolski and Vasily Vasyunin
11. Liftings of kernels shift-invariant in scattering systems Cora Sadosky
12. Some function-theoretic issues in feedback stabilisation Nicholas Young
13. The abstract interpolation problem Alexander Kheifets
14. A basic interpolation problem Harry Dym
15. Reproducing kernel Pontryagin spaces Daniel Alpay, Aad Dijksma, James Rovnyak and Hendrik S. V. de Snoo
16. Commuting operators and function theory on a Riemann surface Victor Vinnikov.

Subject Areas: Geometry [PBM]