An exciting array of both expository and research articles are contained in this volume, which represents the proceedings of a conference on commutative harmonic analysis, held in July 1987 and sponsored by St. Lawrence University and GTE Corporation. The book brings together a host of articles by some of the top researchers in this field and provides an in-depth look at recent progress on many of the diverse areas of current research. Requiring a basic knowledge of Fourier analysis on commutative groups and a familiarity with Euclidean harmonic analysis, this book will be of interest to those beginning research in commutative harmonic analysis. In addition, those currently working in the field will find this book valuable for the broad overview it affords of this important research area.
Spaces of entire functions with no proper translation invariant subspaces by A. Atzmon Gabor representations and wavelets by J. J. Benedetto Measurements of interdependencies of stochastic increments by R. C. Blei Translation-invariant subspaces of weighted $L^p$ by Y. Domar A survey of $k$-plane transforms by S. W. Drury Mixed-norm conditions and Lorentz norms by R. C. Blei and J. F. Fournier Summary of some results on $L^p$-improving measures by C. C. Graham On the $f$- and $K$-properties of certain function spaces by H. Hedenmalm Laplace representation of functions in mixed weighted Bergman by H. P. Heinig and G. J. Sinnamon Equivalence of Riesz products by S. Kilmer Universal trigonometric series with rapidly decreasing coefficients by T. W. Korner A hypergroup measure algebra that admits no analogue of the structure theorem of J. L. Taylor by W. C. Lang Continuity of translation and separable invariant subspaces of Banach spaces associated to locally compact groups by C. C. Graham, A. T.-M. Lau, and M. Leinert Harmonic analysis on functions with bounded means by Y.-Z. Chen and K.-S. Lau Gaussian sums and harmonic analysis on finite fields by O. C. McGehee Quasi-invariant measures and Fourier properties by J.-F. Mela Stability of (deterministic) adaptive auto-regressive filters by L. T. Ramsey Some applications of Khintchin's inequalities by S. Saeki Certain measures on locally compact abelian groups by E. Sato Torsion and torsion-free hypergroups by R. Vrem Weak $S$-sets and Helson sets by C. R. Warner An asymptotic characterization of harmonic functions by Y. Weit Weighted inequalities for the square function by J. M. Wilson.