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Type of Document Dissertation Author Chailuek, Kamthorn Author's Email Address ckamthorn@hotmail.com URN etd-07192007-033805 Title An Extension of Bergman Spaces and their Toeplitz Operators Degree Doctor of Philosophy Department Mathematics Advisory Committee
Advisor Name Title Brian C. Hall Committee Chair Keywords
- Holomorphic function
- Quantization
- Toeplitz operator
- Bergman space
- Space extension
- Hilbert space
Date of Defense 2007-06-25 Availability unrestricted Abstract A Bergman space HL^2(B^d, du_eta) is
non-zero if and only if eta>-1. We define new spaces,
HL^2(B^d,eta), which are the same as Bergman spaces
if eta>-1 but non-zero for eta>-(d+1). We define Toeplitz
operators associated with polynomials to the spaces
HL^2(B^d,eta) when -(d+1)<eta =< -1. We can show
that some properties of Toeplitz operators do not hold in this
range. We also use some properties of Berezin transforms and
Hilbert-Schmidt operators to extend the definition of Toeplitz
operators associated with L^2(B^d, d au), where d au
is the hyperbolic volume measure, to the spaces
HL^2(B^d,eta) when -(d+2)/2<eta=< -1.
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