On the point-spectra of adjoints of composition operators and weighted composition operators
Abstract
The main part of this thesis, Chapter 3, contains results on the point-spectrum of adjoints of certain composition operators and weighted composition operators on the Hardy-Hilbert space, for which the composition map has two distinguished fixed points: one inside the unit disk and one on the unit circle. In particular, we show that the point-spectrum of such operators contains a disk centered at the origin, and each eigenvalue in that disk has infinite multiplicity. We also identify for every such operator a subspace of the Hardy-Hilbert space which is invariant for the operator and on which it acts like a weighted shift.
Degree
Ph.D.
Advisors
Cowen, Purdue University.
Subject Area
Applied Mathematics|Mathematics
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