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Xv Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . xxv Mathematical Family Tree of Lawrence W. Baggett . . . . . . xxvii . Publications of Lawrence W. Baggett . . . . . . . . . . . . . xxix Co-workers of Lawrence W. Baggett . . . . . . . . . . . . . xxxiii . Titles of All Talks . . . . . . . . . . . . . . . . . . . . . . xxxv . I Classical and Abstract Harmonic Analysis 1 Some Riemann Sums Are Better Than Others Victor W.

3 2 Gelfand Pairs Associated with Finite Heisenberg Groups Chal Benson and Gail Ratcliff . . . . . . . . . . . . . . . . . 13 3 Groups with Atomic Regular Representation Keith F. Taylor . . . . . . . . . . . . . . . . . . . . . . . 33 4 Wavelet Transforms and Admissible Group Representations Eric Weber . . . . . . . . . . . . . . . . . . . . . . . . . 47 II Frames and Multiresolution Structures 5 The Density Theorem and the Homogeneous Approximation Property for Gabor Frames Christopher Heil .

Let N be a subgroup of Vs(q> F). Then (N> K) is a Gelfand pair if and only if (C[W]N > _ ) is commutative for all  5 F× . Proof. First note that (C[W]N > _0 ) is, in any case, commutative since _0 is the standard (untwisted) convolution on C[W]. 6 and the the obvious identity (n · i )d = n · id > (n 5 Vs(q> F)> i 5 C[K]> d 5 F). t u 20 Chal Benson and Gail Ratclig Two immediate but useful properties of Gelfand pairs are noted in the following lemma. 11. Let N1 and N2 be a pair of subgroups of Vs(q> F) and suppose that (N1 > K) a Gelfand pair.

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A Robust Embedded Data from Wavelet Coefficients by Chae Manjunath


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