Commutative Harmonic Analysis II

1. Front Matter

   Pages I-9

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2. Convolution and Translation in Classical Analysis

   • V. P. Havin, N. K. Nikolski

   Pages 10-158

3. Invariant Integration and Harmonic Analysis on Locally Compact Abelian Groups

   • V. P. Havin, N. K. Nikolski

   Pages 159-298

4. Back Matter

   Pages 299-328

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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 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 this volume can hardly be found.

• Dualitätstheorie
• Harmonische Analyse
• calculus
• duality theory
• fourier operator
• harmonic analysis
• integration
• locally compact abelian groups
• lokal kompakte abelsche Gruppen
• operator
• translation invariant subspaces
• translationsinvariante Unterräume

• Department of Mathematics, St. Petersburg State University, St. Petersburg, Staryj Peterhof, Russia

  V. P. Havin

• Department of Mathematics and Statistics, McGill University, Montreal, Canada

  V. P. Havin

• Steklov Mathematical Institute, St. Petersburg, Russia

  N. K. Nikolski

• Département de Mathématiques, Université de Bordeaux I, Talence, Cedex, France

  N. K. Nikolski

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