Decay of the Fourier Transform Analytic and Geometric Aspects /

• Main Authors: Iosevich, Alex (Author), Liflyand, Elijah (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2014.
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Fourier analysis.; Analysis.; Fourier Analysis.

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 an...

Table of Contents:

• 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.