Brief description of research:
My research is in complex analysis. I am particularly interested in the study of linear operators on spaces of analytic functions. The operators include multiplication operators, composition operators, and conditional expectation operators. The spaces of functions include the Bergman spaces, Hardy spaces, and Fock spaces. Of interest is the interplay between the properties of a operator and the types of functions it acts on.
Publications:
(6) Bergman projection and disintegration of Lebesgue area measure (with M. Stessin), submitted.
(5) Conditional expectation and the Bergman projection (with M. Stessin), to appear in J. Math. Anal. Appl.
(4) Composition operators with maximal norm on weighted Bergman spaces (with C. Hammond), Proc. Amer. Math. Soc. 134 (2006), no. 9, 2599-2605. (.pdf)
(3) Composition operators on the Fock space
(with B. MacCluer and A. Schuster), Acta Sci. Math. (
(2) Univalent mappings and invariant subspaces of the Hardy and Bergman spaces, Proc. Amer. Math. Soc. 131 (2003), no. 4, 1233-1241. (.pdf)
(1) Multiplication invariant subspaces of the Bergman space (with P. Duren and M. Stessin), Indiana University Math. J. 51 (2002), no. 4, 931-961. (.pdf)
(0) Wandering property for Bergman submodules
over singly generated algebras, Ph.D. thesis, University at
Conference Co-organized: Recent
advances in operator-related function theory,
Here is a list of 121 people whom I've met whose research is connected to my own: