Type of Document 
Dissertation 
Author 
Ho, Vivian Mankau

Author's Email Address 
vivian@math.lsu.edu 
URN 
etd07122012095333 
Title 
PaleyWiener Theorem for Line Bundles over Compact Symmetric Spaces 
Degree 
Doctor of Philosophy (Ph.D.) 
Department 
Mathematics 
Advisory Committee 
Advisor Name 
Title 
Ólafsson, Gestur 
Committee Chair 
Davidson, Mark 
Committee Member 
He, Hongyu 
Committee Member 
Hoffman, Jerome 
Committee Member 
Litherland, Richard 
Committee Member 
Wu, HsiaoChun 
Dean's Representative 

Keywords 
 $chi$spherical representations
 invariant differential operators
 PaleyWiener Theorem
 compact symmetric spaces
 $chi$spherical Fourier transforms
 hypergeometric functions

Date of Defense 
20120629 
Availability 
unrestricted 
Abstract
We generalize a PaleyWiener theorem to homogeneous line bundles $L_\chi$ on a compact symmetric space U/K with $\chi$ a nontrivial character of K. The Fourier coefficients of a $\chi$bicoinvariant function f on U are defined by integration of f against the elementary spherical functions of type $\chi$ on U, depending on a spectral parameter $\mu$, which in turn parametrizes the $\chi$spherical representations $\pi$ of U. The PaleyWiener theorem characterizes f with sufficiently small support in terms of holomorphic extendability and exponential growth of their $\chi$spherical Fourier transforms. We generalize Opdam's estimate for the hypergeometric functions in a bigger domain with the multiplicity parameters being not necessarily positive, which is crucial to the proof of PaleyWiener theorem in our case.

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