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.
This book is a collection of expository articles arising from MSRI’s fall 1995 program on holomorphic spaces. The opening article, by Donald Sarason, gives an overview of several aspects of the subject. The remaining articles, while more specialized, are nevertheless designed in varying degrees to be accessible to the nonexpert; some are minicourses in themselves. A range of topics is discussed:
- Bergman spaces
- Hankel operators in various guises
- the Dirichlet space
- subnormal operators
- operator models, interpolation problems, systems theory
- commuting families of nonselfadjoint operators
- Complete contents
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