Fourier Series in Several Variables with Applications to Partial Differential Equations

ISBN-13: 9781439854273 / Angielski / Twarda / 2011 / 352 str.

Victor Shapiro;¬Abar;¬Abar

Opis

Presenting Fourier series from the aspect of several variables, this book covers connections between Fourier analysis and partial differential equations. It discusses newly emerging topics, such as the fundamental results on Calderon-Zygmund kernels in multi-dimensions and their relation to Fourier series and integrals, along with Fourier integrals and their applications to uniqueness for two-dimensional trigonometric series. The author explores important applications for the first time through reaction-diffusion equations and Navier-Stokes equations. The text also covers spherical harmonics and includes problems to aid with application.

Spis treści

Summability of Multiple Fourier Series. Conjugate Multiple Fourier Series. Uniqueness of Multiple Trigonometric Series. Positive Definite Functions. Nonlinear Partial Differential Equations. The Stationary Navier-Stokes Equations. Appendices. Bibliography. Index.

O autorze

Victor L. Shapiro is a Distinguished Professor Emeritus in the Department of Mathematics at the University of California, Riverside, where he has taught for 46 years. He earned his Ph.D. from the University of Chicago and completed postdoctoral work at the Institute for Advanced Study, where he was an NSF fellow.