Fourier Series in Several Variables with Applications to Partial Differential Equations

ISBN-13: 9780367382926 / Angielski / Miękka / 2019 / 352 str.

Victor Shapiro

Opis

Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear PDEs. Using these methods, the author presents results for stationary Navier-Stokes equations, nonlinear reaction-diffusion systems, and quasilinear elliptic PDEs and resonance theory. He also establishes the connection between multiple Fourier series and number theory, presents the periodic C^α-theory of Calderon and Zygmund, and explores the extension of Fatou’s famous work on antiderivatives and nontangential limits to higher dimensions. The importance of surface spherical harmonic functions is emphasized throughout.

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.