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Some Notes on the Theory of Hilbert Spaces of Analytic Functions on the Unit Disc

by Silva Jorg

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Institution: University of California at Berkeley
Advisor(s): D. Sarason
Degree: Ph.D., Mathematics
Year: 1994
Volume: 19 pages
ISBN-10: 1581120230
ISBN-13: 9781581120233

Abstract

In this work we explore the relation between some local Dirichlet spaces and some operator ranges. As an application we give numerical bounds for an equivalence of norms on a particular subspace of the Hardy space.

Based on these results we introduce an operator on H^2 which we study in some detail.

We also introduce a Hilbert space of analytic functions on the unit disc, prove the polynomials are dense in it, and give a characterization of its elements.

On these spaces we study the action of composition operators induced by holomorphic self maps of the disc. We give characterizations of the bounded and compact ones in terms of the behavior of the inducing maps.

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