Fourier Analysis and Partial Differential Equations [Hardcover]

A 2001 introduction to Fourier analysis and partial differential equations; aimed at beginning graduate students.This modern introduction to Fourier analysis and partial differential equations is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations, including a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations. In the two final chapters they turn their attention to the non-periodic setting, concentrating on problems that do not occur in the periodic case.This modern introduction to Fourier analysis and partial differential equations is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations, including a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations. In the two final chapters they turn their attention to the non-periodic setting, concentrating on problems that do not occur in the periodic case.This modern introduction to Fourier analysis and partial differential equations is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations, including a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations; they turn their attention, in the two final chapters, to the nonperiodic setting, concentrating on problems that do not occur in the periodic case.Part I. Fourier Series and Periodic Distributions: 1. Preliminaries; 2. Fourier series: basic theory; 3. Periodic distributions and Soboll³‡