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| Preface Part One: Fourier Series and Periodic Distributions 1 Preliminaries 1.1 Basic Definitions and Examples 1.2 Classification into Types 1.3 Boundary and/or Initial Value Problems 1.4 Separation of Variables: Heat Flow in a Bar 1.5 The Schrodinger and the Wave Equations 1.6 The Dirichlet Problem in the Unit Circle 1.7 Maximum Principles and Uniqueness 2 Fourier Series: Basic Theory 2.1 Spaces of Periodic Functions and Sequences 2.2 The Fourier Transform 2.3 Geometric Interpretation 2.4 Decay and Differentiability 2.5 The Inversion Formula: Pointwise Convergence 2.6 Periodic Heat Flow 2.7 Approximate Identities and Summability 2.8 Cesaro Summability 3 Periodic Distributions and Sobolev Spaces 3.1 C Peiodic Funcitons 3.2 Perodic Distributions 3.3 Topological Remakes 3.4 Fourier Series in 3.5 The Convolution in 3.6 Sobolev Spaces Part Two:Applications to Partial Dfferential Equations 4 Linear Equations 5 Nonlinear Evolution Equations 6 The Korteweg-de Vries Equation 7 Distributions,Fourier Transform and Linear Equations 8 KdV,BO and Friends Appendix A Tools from the Theory of ODEs Appendix B Commutator Estimates Bibliography Index |
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