Shapiro V.L. Fourier series in several variables with applications to partial differential equations. - Boca Raton; London: Chapman & Hall/CRC, 2011. - xiv, 338 p. - (Chapman & Hall/CRC applied mathematics and nonlinear science series). - Bibliogr.: p.331-334. - Ind.: p.335-338. - ISBN 978-1-4398-5427-3  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Preface ....................................................... vii Chapter 1. Summability of Multiple Fourier Series ............... 1 1 Introduction ................................................. 1 2 Iterated Fejer Summability of Fourier Series ................. 2 3 Bochner-Riesz Summability of Fourier Series .................. 8 4 Abel Summability of Fourier Series .......................... 16 5 Gauss-Weierstrass Summability of Fourier Series ............. 29 6 Further Results and Comments ................................ 36 Chapter 2. Conjugate Multiple Fourier Series ................... 39 1 Introduction ................................................ 39 2 Abel Summability of Conjugate Series ........................ 48 3 Spherical Convergence of Conjugate Series ................... 56 4 The Cα-Condition ............................................ 66 5 An Application of the Cα-Condition .......................... 70 6 An Application of the Lp-Condition .......................... 74 7 Further Results and Comments ................................ 78 Chapter 3. Uniqueness of Multiple Trigonometric Series ......... 79 1 Uniqueness for Abel Summability ............................. 79 2 Uniqueness for Circular Convergence ......................... 96 3 Uniqueness, Number Theory, and Fractals .................... 102 4 Further Results and Comments ............................... 136 Chapter 4. Positive Definite Functions ........................ 139 1 Positive Definite Functions on SN-1 ........................ 139 2 Positive Definite Functions on TN .......................... 143 3 Positive Definite Functions on SN1-1 × ТN ................... 148 4 Further Results and Comments ............................... 156 Chapter 5. Nonlinear Partial Differential Equations ........... 159 1 Reaction-Diffusion Equations on the N-Torus ................ 159 2 Quasilinear Ellipticity on the N-Torus ..................... 186 3 Further Results and Comments ............................... 215 Chapter 6. The Stationary Navier-Stokes Equations ............. 219 1 Distribution Solutions ..................................... 219 2 Classical Solutions ........................................ 259 3 Further Results and Comments ............................... 271 Appendix А. Integrals and Identities .......................... 277 1 Integral Identities ........................................ 277 2 Estimates for Bessel Functions ............................. 281 3 Surface Spherical Harmonics ................................ 284 Appendix В. Real Analysis ..................................... 299 1 Convergence and Summability ................................ 299 2 Tauberian Limit Theorems ................................... 301 3 Distributions on the N-Torus .............................. 305 4 Hj(x) and the Cα-Condition ................................. 310 Appendix C. Harmonic and Subharmonic Functions ................ 315 1 Harmonic Functions ......................................... 315 2 Subharmonic Functions ...................................... 326 Bibliography .................................................. 331 Index ......................................................... 335