Decay of the Fourier Transform (eBook)

Analytic and Geometric Aspects

Alex Iosevich, Elijah Liflyand (Autoren)

eBook Download: PDF

2014 | 2014
XII, 222 Seiten
Birkhäuser Verlag GmbH
978-3-0348-0625-1 (ISBN)

Infos

The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 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 L^2 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.​

Inhalt

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.​

Produkt-Details

• Erscheint lt. Verlag: 1.10.2014
• Zusatzinfo: XII, 222 p. 5 illus., 2 illus. in color.
• Verlagsort: Basel
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• Schlagworte: Bounded Variation • Curvature • decay rate • Fourier transform • spherical average
• ISBN-10: 3-0348-0625-6 / 3034806256
• ISBN-13: 978-3-0348-0625-1 / 9783034806251