Decay of the Fourier Transform: Analytic and Geometric Aspects
Autor Alex Iosevich, Elijah Liflyanden Limba Engleză Hardback – 10 oct 2014
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Specificații
ISBN-13: 9783034806244
ISBN-10: 3034806248
Pagini: 350
Ilustrații: XII, 222 p. 5 illus., 2 illus. in color.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.51 kg
Ediția:2014
Editura: Springer
Colecția Birkhäuser
Locul publicării:Basel, Switzerland
ISBN-10: 3034806248
Pagini: 350
Ilustrații: XII, 222 p. 5 illus., 2 illus. in color.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.51 kg
Ediția:2014
Editura: Springer
Colecția Birkhäuser
Locul publicării:Basel, Switzerland
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Public țintă
ResearchCuprins
Foreword.- Introduction.- Chapter 1. Basic properties of the Fourier transform.- Chapter 2. Oscillatory integrals and Fourier transforms in one variable.- Chapter 3. The Fourier transform of an oscillating function.- Chapter 4. The Fourier transform of a radial function.- Chapter 5. Multivariate extensions.- Appendix.- Bibliography.
Recenzii
“The overall presentation is clear and the reader is carefully guided through this territory which is marked by a beautiful blend of ideas and techniques from analysis, geometry and also number theory.” (Wien R. Steinbauer, Monatshefte für Mathematik, Vol. 185, 2018)
“It is an introduction to current topics in Fourier analysis, to be read and appreciated by mathematicians … . the book is carefully designed and well written. It does a very good job of familiarizing the reader with the relevant techniques and results, relying on a beautiful interplay of analysis, geometry and number theory.” (Hartmut Führ, Mathematical Reviews, January, 2016)
“It is an introduction to current topics in Fourier analysis, to be read and appreciated by mathematicians … . the book is carefully designed and well written. It does a very good job of familiarizing the reader with the relevant techniques and results, relying on a beautiful interplay of analysis, geometry and number theory.” (Hartmut Führ, Mathematical Reviews, January, 2016)
Textul de pe ultima copertă
The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
Caracteristici
Only book where the decay rate of the Fourier transform is the dominant theme Systematic examination of the concepts Focus on interaction between the analytic and geometric approaches of Fourier theory?