Download Fourier Series in Several Variables with Applications to by Victor Shapiro PDF

By Victor Shapiro

Fourier sequence in numerous Variables with purposes to Partial Differential Equations illustrates the worth of Fourier sequence tools in fixing tough nonlinear partial differential equations (PDEs). utilizing those equipment, the writer offers effects for desk bound Navier-Stokes equations, nonlinear reaction-diffusion structures, and quasilinear elliptic PDEs and resonance idea. He additionally establishes the relationship among a number of Fourier sequence and quantity theory.

The booklet first offers 4 summability equipment utilized in learning a number of Fourier sequence: iterated Fejer, Bochner-Riesz, Abel, and Gauss-Weierstrass. It then covers conjugate a number of Fourier sequence, the analogue of Cantor’s forte theorem in dimensions, floor round harmonics, and Schoenberg’s theorem. After describing 5 theorems on periodic ideas of nonlinear PDEs, the textual content concludes with recommendations of desk bound Navier-Stokes equations.

Discussing many effects and experiences from the literature, this e-book demonstrates the powerful strength of Fourier research in fixing doubtless impenetrable nonlinear problems.

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