โ Scribed by V. P. Havin, N. K. Nikolski (auth.), V. P. Havin, N. K. Nikolski (eds.)
No coin nor oath required. For personal study only.
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 (and still does), conquering new unexpected areas and producing impressive applications to a multitude of problems, old and new, ranging from arithmetic to optics, from geometry to quantum mechanics, not to mention analysis and differential equations. The power of group theoretic ideology is successfully illustrated by this wide range of topics. It is widely understood now that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This volume is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in the present volume can hardly be found in any monograph. This book will be very useful to a wide circle of readers, including mathematicians, theoretical physicists and engineers.
Front Matter....Pages I-9
Convolution and Translation in Classical Analysis....Pages 10-158
Invariant Integration and Harmonic Analysis on Locally Compact Abelian Groups....Pages 159-298
Back Matter....Pages 299-328
Analysis
๐ SIMILAR VOLUMES
This monograph discusses nonstandard analysis (NSA) and its applications to harmonic analysis on locally compact Abelian (LCA) groups. A new notion of approximation of topological groups by finite groups is introduced and investigated. Based on this notion, new results are obtained on convergence of
This monograph discusses nonstandard analysis (NSA) and its applications to harmonic analysis on locally compact Abelian (LCA) groups. A new notion of approximation of topological groups by finite groups is introduced and investigated. Based on this notion, new results are obtained on convergence of
This monograph discusses nonstandard analysis (NSA) and its applications to harmonic analysis on locally compact Abelian (LCA) groups. A new notion of approximation of topological groups by finite groups is introduced and investigated. Based on this notion, new results are obtained on convergence of
With the groundwork laid in the first volume (EMS 15) of the Commutative Harmonic Analysis subseries of the Encyclopaedia, the present volume takes up four advanced topics in the subject: Littlewood-Paley theory for singular integrals, exceptional sets, multiple Fourier series and multiple Fourier i