Fourier Analysis and Partial Differential Equations

Cambridge Studies in Advanced Mathematics #70

by Rafael José Iorio Jr., Valéria de Magalhães Iorio

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.

424 pages, Paperback

First published March 15, 2001

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Aparece (escrito de manera amigable) el espacio de Sobolev definido sobre el círculo mediante series de Fourier.

Theorem 3.200 If s>1/2, the space H_per^s is a Banach algebra

Example 3.20 The function f_lambda(x)=1/|x|^lambda defines a periodic distribution