Fourier Analysis Analytic and Geometric Aspects Lecture Notes in Pure and Applied Mathematics Series

Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.

Preface -- Contributors -- 1. Ergodic and Mixing Properties of Radial Measures on the Heisenberg Group Mark /Agranovsky, Carlos Berenstein, and Der-Chen Chang -- 2. IF and Weak IF Continuity of Calderon-Zygmund Type Operators /Josefina Alvarez -- 3. A New, Harder Proof That Continuous Functions with Schwarz Derivative 0 Are Lines /J. Marshall Ash -- 4. Integrability of Multiple Series /Bruce Aubertin and John J. F. Fournier -- 5. Aspects of Harmonic Analysis on Real Hyperbolic Space /William O. Bray -- 6. Trace Theorems via Wavelets on the Closed Set [0, 1] /Anca Deliu and Mong-Shu Lee -- 7. Meta-Heisenberg Groups /Gerald B. Folland -- 8. Numerical Approximation of Singular Spectral Functions Arising from the Fourier-Jacobi Problem on a Half Line with Continuous Spectra /Charles T. Fulton and Steven Pruess -- 9. Using Sums of Squares to Prove That Certain Entire Functions Have Only Real Zeros /George Gasper -- 10. An Application of Coxeter Groups to the Construction of Wavelet Bases in R1 /Jeffrey S. Geronimo, Douglas P. Hardin, and Peter R. Massopust -- 11. The Uniform Invertibility of Fourier Transforms of Compositions of Functions in 21 (R2) with Certain Quadratic Maps of R2 /Peter M. Jarvis -- 12. On Methods of Fourier Analysis in Multigrid Theory /Erwin Kreyszig -- 13. Orthogonal Wavelet Bases for L^R1) /W. A. Madych -- 14. The Fourier Transform of Tempered Boehmians /Piotr Mikusinski -- 15. Approximation-Solvability of Nonlinear Equations and Applications /P. S. Milojevic -- 16. Homogeneous Cones and Homogeneous Integrals /Tatjana Ostrogorski -- 17. Fourier Inversion in the Piecewise Smooth Category /Mark A, Pinsky -- 18. Normed Linear Spaces of Trigonometric Transforms and Functions Analytic in the Unit Disk /Caslav V. Stanojevic -- 19. Fourier and Trigonometric Transforms with Complex Coefficients Regularly Varying in Mean /Vera B. Stanojevic -- 20. Sampling and the Multisensor Deconvolution Problem /David F. Walnut.

Professional

WILLIAM O. Bray is an Associate Professor of Mathematics at the University of Maine, Orono. The author of numerous professional papers in the area of Fourier/harmonic analysis, he is a member of the American Mathematical Society and the Mathematical Association of America. Dr. Bray received the Ph.D. degree (1981) in mathematics from the University of Missouri—Rolla. P. S. MILOJEVIC is Professor of Mathematics at the New Jersey Institute of Technology in Newark. The editor of the book Nonlinear Functional Analysis (Marcel Dekker, Inc.), his primary area of research is nonlinear functional analysis and its applications and he has published extensively in this field. Dr. Milojevic is a member of the American Mathematical Society. He received the Ph.D. degree (1975) from Rutgers University, New Brunswick, New Jersey. CASLAV V. STANOJEVIC is Distinguished Professor in the Department of Mathematics and Statistics, University of Missouri—Rolla. The founder of the International Workshop in Analysis and its Applications (IWAA) and Chairman of the Organization Committee of IWAA, he is the author of numerous research papers in various areas of mathematics, and the holder of a U.S. patent. Dr. Stanojevic received the Ph.D. degree (1955) from the University of Belgrade, Yugoslavia.