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Fourier Series in Several Variables with Applications to Partial Differential Equations

Victor L. Shapiro
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2011
Number of Pages: 
338
Format: 
Hardcover
Series: 
Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series
Price: 
99.95
ISBN: 
9781439854273
Category: 
Monograph
We do not plan to review this book.

Summability of Multiple Fourier Series
Introduction
Iterated Fejer Summability of Fourier Series
Bochner-Riesz Summability of Fourier Series
Abel Summability of Fourier Series
Gauss-Weierstrass Summability of Fourier Series
Further Results and Comments

Conjugate Multiple Fourier Series
Introduction
Abel Summability of Conjugate Series
Spherical Convergence of Conjugate Series
The Cα-Condition
An Application of the Cα-Condition
An Application of the Lp–Condition
Further Results and Comments

Uniqueness of Multiple Trigonometric Series
Uniqueness for Abel Summability
Uniqueness for Circular Convergence
Uniqueness, Number Theory, and Fractals
Further Results and Comments

Positive Definite Functions
Positive Definite Functions on SN-l
Positive Definite Functions on TN
Positive Definite Functions on SN1-l × TN
Further Results and Comments

Nonlinear Partial Differential Equations
Reaction-Diffusion Equations on the N-Torus
Quasilinear Ellipticity on the N-Torus
Further Results and Comments

The Stationary Navier-Stokes Equations
Distribution Solutions
Classical Solutions
Further Results and Comments

Appendix A: Integrals and Identities
Appendix B: Real Analysis
Appendix C: Harmonic and Subharmonic Functions

 

Bibliography

Index

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