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Analysis Seminar

SPEAKER: Prof. Marie Neophytou, Belmont University

TITLE: Eigenvalues of the Adjoints of Some Composition Operators and Weighted Composition Operators

ABSTRACT: Let H be the Hardy-Hilbert space of analytic functions on the unit disk. If ϕ is an analytic map of the unit disk into itself and ψ is analytic on the disk, the composition operator Cϕ with symbol ϕ is defined by Cϕ f = f ◦ ϕ, and the weighted composition operator Wψ,ϕ by Wψ,ϕ f = ψ(f ◦ ϕ), for f in H 2 .

We look at adjoints of composition operators with symbols ϕ that have a fixed point inside the disk and a fixed point on the boundary with finite angular derivative there. By imposing a few extra assumptions on ϕ, we show that the point spectrum of the adjoint contains a disk centered at the origin, and that the corresponding eigenspaces are infinite-dimensional. We also identify a subspace of H 2 which is invariant for the adjoint and on which the adjoint acts like a weighted shift. Finally, we generalize these results to weighted composition operators.

Where

Ayres Hall

Room 112
1403 Circle Drive
Knoxville, TN 37996
USA

When

Wednesday, 05 March, 2014

Who to contact

Contact:

Betty Morgan

Phone: 974-2463