| Type of Document |
Dissertation |
| Author |
Ho, Vivian Mankau
|
| Author's Email Address |
vivian@math.lsu.edu |
| URN |
etd-07122012-095333 |
| Title |
Paley-Wiener 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, Hsiao-Chun |
Dean's Representative |
|
| Keywords |
- $chi$-spherical representations
- invariant differential operators
- Paley-Wiener Theorem
- compact symmetric spaces
- $chi$-spherical Fourier transforms
- hypergeometric functions
|
| Date of Defense |
2012-06-29 |
| Availability |
unrestricted |
Abstract
We generalize a Paley-Wiener 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 $\chi$-bi-coinvariant 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 Paley-Wiener 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 Paley-Wiener theorem in our case.
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