Spectral Properties of a Class of Integral Operators on Spaces of Analytic Functions

Author

Snehalatha Ballamoole

Issuing Body

Mississippi State University

Advisor

Miller, T. Len

Committee Member

Sepehrifar, Mohammad

Committee Member

Dobson, Edward T.

Committee Member

Neumann, Michael M.

Committee Member

Smith, Robert C.

Other Advisors or Committee Members

Miller, Vivien G.

Date of Degree

8-15-2014

Document Type

Dissertation - Open Access

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

Spectral properties of integral operators on spaces of analytic functions on the unit disk of the complex plane have been studied since 1918. In this dissertation we determine spectral pictures and resolvent estimates for Ces`aro-like operators on the weighted Bergman spaces and show in particular that some of these operators are subdecomposable. Moreover, in a special case, we show that some of these operators are subnormal, some are normaloid, and some are subscalar. We also determine the spectrum and essential spectrum as well as resolvent estimates for a class of integral operators acting on Banach spaces of analytic functions on the unit disk, including the classical Hardy and weighted Bergman spaces, analytic Besov spaces as well as certain Dirichlet spaces and generalized Bloch spaces. Our results unify and extend recent work by Aleman and Persson, [4], Ballamoole, Miller and Miller, [6], and Albrecht and Miller, [3]. In [3], another class of integral operators were investigated in the setting of the analytic Besov spaces and the little Bloch space where the spectra, essential spectra together with one sided analytic resolvents in the Fredholm regions of these operators were obtained along with an explicit strongly decomposable operator extending one of these operator and simultaneously lifting the other. In this disseration, we extend this spectral analysis to nonseparable generalized Bloch spaces using a modification of a construction due to Aleman and Persson, [4].

URI

https://hdl.handle.net/11668/19888

Comments

Cesaro operator||decomposability||resolvent||spectrum||spectral properties||Integral operators

Recommended Citation

Ballamoole, Snehalatha, "Spectral Properties of a Class of Integral Operators on Spaces of Analytic Functions" (2014). Theses and Dissertations. 4024.
https://scholarsjunction.msstate.edu/td/4024