This book explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations. It began as lecture notes for a one-semester graduate course given by the author in noncommutative harmonic analysis. It is a valuable resource for both graduate students and faculty, and requires only a background with Fourier analysis and basic functional analysis, plus the first few chapters of a standard text on Lie groups. The basic method of noncommutative harmonic analysis, a generalization of Fourier analysis, is to synthesize operators on a space on which a Lie group has a unitary representation from operators on irreducible representation spaces.Though the general study is far from complete, this book covers a great deal of the progress that has been made on important classes of Lie groups. Unlike many other books on harmonic analysis, this book focuses on the relationship between harmonic analysis and partial differential equations. The author considers many classical PDEs, particularly boundary value problems for domains with simple shapes, that exhibit noncommutative groups of symmetries. Also, the book contains detailed work, which has not previously been published, on the harmonic analysis of the Heisenberg group and harmonic analysis on cones.
Acoustics and the Performance of Music addresses issues that are of interest to acousticians, orchestra performers and conductors, audio engineers, architects. Researchers and students of musical acoustics will also find this text valuable.
Noncommutative Microlocal Analysis
Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody ...
K*(A, u, l,g)= KÍ(u, Xil, g=1). ... The Group SL(2,R) and Pollaczek—Meixner Polynomials. The function T(2u + n) • –2i P'(x; p)= #e"F(-nt +ix;2u; 1 – e'”) is a polynomial of degree n in a, called the Pollaczek—Meixner polynomial.
This volume contains the proceedings of the AMS Special Session on Wavelet and Frame Theoretic Methods in Harmonic Analysis and Partial Differential Equations, held September 22-23, 2012, at the Rochester Institute of Technology, Rochester, ...
Annotation All the papers in this volume are research papers presenting new results. Most of the results concern semi-simple Lie groups and non-Riemannian symmetric spaces: unitarisation, discrete series characters, multiplicities,...
I would like to believe that others can be led to see this picture by reading my paper, and to facilitate this I have included a large number of short expositions of topics which are not widely understood by non-specialists.'' --from the ...
These are used in the last two chapters. The first covers the Heisenberg group which encode the Heisenberg uncertainty principle. This is first instance of the use of infinite dimensional representations.
'This is a book to be read and worked with.