- eBook:Fourier Analysis: An Introduction (Princeton Lectures in Analysis, Volume 1)
- Author:Elias M. Stein, Rami Shakarchi
- Data:April 6, 2003
- Pages:328 pages
The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.
In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest.
The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Chapter 2. Basic Properties of Fourier Series
Chapter 3. Convergence of Fourier Series
Chapter 4. Some Applications of Fourier Series
Chapter 5. The Fourier Transform on R
Chapter 6. The Fourier Transform on Rd
Chapter 7. Finite Fourier Analysis
Chapter 8. Dirichlet's Theorem