Fourier Analysis and Its Applications

Gerald B. Folland, University of Washington, Seattle, WA, USA

The book is a detailed and very readable treatise on the theory and practice of series expansions and transforms. The primary audience consists of advanced undergraduates in mathematics, physics, and engineering, but the book is also a useful reference for more advanced workers . . . The strength of the book comes from its careful presentation of theory followed by detailed applications, with good illustrations, and finally a generous collection of exercises (with answers). The prose is smooth and gives understandable discussions of technical difficulties . . . This text can surely be recommended for use in a one or two semester course, or as a reference for graduate students or other persons who want to see what sort of problems Fourier analysis was invented to solve." - C. F. Dunkl, Zentralblatt MATH"With the same mastery as in his Real analysis, the author now offers us this excellent textbook on Fourier analysis: Fourier series, orthogonal systems, Bessel functions, Fourier and Laplace transforms, which are all very powerful mathematical tools in many a scientific domain. Without being exhaustive and without falling into a profusion of boring details, it nevertheless gives a panorama of these topics that is as complete as the framework of the book allows. Thus this text, which is designed for courses at the advanced undergraduate level and beyond, will also serve as a useful reference book." - Mathematical Reviews

• PrefaceContentsChapter 1. OvertureChapter 2. Fourier seriesChapter 3. Orthogonal sets of functionsChapter 4. Some boundary value problemsChapter 5. Bessel functionsChapter 6. Orthogonal polynomialsChapter 7. The Fourier transformChapter 8. The Laplace transformChapter 9. Generalized functionsChapter 10. Green’s functionsAppendicesAnswers to the ExercisesReferencesIndex of SymbolsIndex