This EMS volume shows the great power provided by modern harmonic analysis, not only in mathematics, but also in mathematical physics and engineering. Aimed at a reader who has learned the principles of harmonic analysis, this book is intended to provide a variety of perspectives on this important classical subject. The authors have written an outstanding book which distinguishes itself by the authors' excellent expository style. It can be useful for the expert in one area of harmonic analysis who wishes to obtain broader knowledge of other aspects of the subject and also by graduate students...

The theory of generalized functions is a general method that makes it possible to consider and compute divergent integrals, sum divergent series, differentiate discontinuous functions, perform the operation of integration to any complex power and carry out other such operations that are impossible in classical analysis. Such operations are widely used in mathematical physics and the theory of differential equations, where the ideas of generalized func tions first arose, in other areas of analysis and beyond. The point of departure for this theory is to regard a function not as a mapping of...

Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very...