Adjoints of Composition Operators on Hardy Spaces of the Half-Plane

Details Adjoints of Composition Operators on Hardy Spaces of the Half-Plane Adjoints of Composition Operators on Hardy Spaces of the Half-Plane

2008-10-13

arxiv.org/abs/0810.2184v1

Mathematics

Functional Analysis

20 pages, Submitted to Elsevier

Scientific paper

Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known necessary condition for the boundedness of such operators, and use it to provide a complete classification of the bounded composition operators with rational symbol. We then consider some specific examples, comparing our formulae with each other, and with other easily deduced formulae for simple cases.

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