A joint project of the Graduate School, Peabody College, and the Jean & Alexander Heard Library

Title page for ETD etd-03232006-005345


Type of Document Dissertation
Author Zhong, Changyong
Author's Email Address changyong.zhong@vanderbilt.edu
URN etd-03232006-005345
Title Multiplication Operators and M-Berezin Transforms
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Dechao Zheng Committee Chair
Dietmar Bisch Committee Member
Edward B. Saff Committee Member
Guoliang Yu Committee Member
Sokrates T. Pantelides Committee Member
Keywords
  • m-Berezin Transforms
  • Reducing Subspaces
  • Toeplitz Operators
  • Hardy Space
  • Bergman Space
Date of Defense 2006-03-20
Availability unrestricted
Abstract
Lattices of reducing subspaces of multiplication operators acting on the Bergman space induced by finite Blaschke products are studied. A complete description of the lattices of reducing subspaces of multiplication operators induced by Blaschke products of order three or order four is given. It is proved that, for the multiplication operator acting on the Bergman space induced by Blaschke product of order three or order four, the number of minimal reducing subspaces equals the number of connected components of the Riemann surface associated to the composition of the inverse of the Blaschke product and the Blaschke product itself.

A characterization about the compactness of certain operators in the Toeplitz algebra acting on Bergman spaces of several complex variables is obtained via m-Berezin transforms.

Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
 28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access 
  thesis.pdf 618.89 Kb 00:02:51 00:01:28 00:01:17 00:00:38 00:00:03

Browse All Available ETDs by ( Author | Department )

If you have more questions or technical problems, please Contact LITS.