โ Scribed by Sh. A. Alimov, R. R. Ashurov, A. K. Pulatov (auth.), V. P. Khavin, N. K. Nikolโskiว (eds.)
No coin nor oath required. For personal study only.
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 integrals. The authors assume that the reader is familiar with the fundamentals of harmonic analysis and with basic functional analysis. The exposition starts with the basics for each topic, also taking account of the historical development, and ends by bringing the subject to the level of current research. Table of Contents I. Multiple Fourier Series and Fourier Integrals. Sh.A.Alimov, R.R.Ashurov, A.K.Pulatov II. Methods of the Theory of Singular Integrals. II: Littlewood Paley Theory and its Applications E.M.Dyn'kin III.Exceptional Sets in Harmonic Analysis S.V.Kislyakov
Front Matter....Pages i-ix
Multiple Fourier Series and Fourier Integrals....Pages 1-95
Methods of the Theory of Singular Integrals: Littlewood-Paley Theory and Its Applications....Pages 97-194
Exceptional Sets in Harmonic Analysis....Pages 195-221
Back Matter....Pages 223-230
Analysis; Topological Groups, Lie Groups
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<p>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 im