Abstract of Talk by Dr. Carl L. Prather

Bandlimited Signals, Quantum Mechanics and Sampling for Entire Functions

Dr. Carl L. Prather
Department of Mathematics
Virginia Polytech Institute & State University  
Blacksburg, VA 24061-0123
(1995-96) On leave at Northwestern University

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First, the Whittaker-Shannon cardinal series for bandlimited signals will be derived with applications to nonharmonic Fourier series given. Secondly, a classical completeness problem for Fock-Gabor coherent states arising in quantum mechanics will be introduced. The solution of these problems involve the use of expansion results for functions in the Bargmann space of analytic functions, as will be explained.

Each of the above topics makes use of sampling theorems for entire functions. Some recent work connected with wavelets will be outlined with generalizations and open questions indicated.

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