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