Fourier Series, Fourier Transform and Their Applications to Mathematical Physics

Table of Contents

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   Book Overview
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   Chapter 1 Introduction
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   Chapter 2 Formulation of Fourier Series
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   Chapter 3 Fourier Coefficients and Their Properties
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   Chapter 4 Convolution and Parseval’s Equality
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   Chapter 5 Fejér Means of Fourier Series. Uniqueness of the Fourier Series.
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   Chapter 6 The Riemann–Lebesgue Lemma
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   Chapter 7 The Fourier Series of a Square-Integrable Function. The Riesz–Fischer Theorem.
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   Chapter 8 Besov and Hölder Spaces
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    Chapter 9 Absolute Convergence. Bernstein and Peetre Theorems.
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    Chapter 10 Dirichlet Kernel. Pointwise and Uniform Convergence.
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    Chapter 11 Formulation of the Discrete Fourier Transform and Its Properties.
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    Chapter 12 Connection Between the Discrete Fourier Transform and the Fourier Transform.
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    Chapter 13 Some Applications of the Discrete Fourier Transform.
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    Chapter 14 Applications to Solving Some Model Equations
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    Chapter 15 Introduction
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    Chapter 16 The Fourier Transform in Schwartz Space
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    Chapter 17 The Fourier Transform in $$L^p(\mathbb {R}^n)$$ , $$1\le p\le 2$$
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    Chapter 18 Tempered Distributions
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    Chapter 19 Convolutions in S and $$S'$$
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    Chapter 20 Sobolev Spaces
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    Chapter 21 Homogeneous Distributions
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    Chapter 22 Fundamental Solution of the Helmholtz Operator
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    Chapter 23 Estimates for the Laplacian and Hamiltonian
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    Chapter 24 Introduction
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    Chapter 25 Inner Product Spaces and Hilbert Spaces
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    Chapter 26 Symmetric Operators in Hilbert Spaces
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    Chapter 27 John von Neumann’s Spectral Theorem
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    Chapter 28 Spectra of Self-Adjoint Operators
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    Chapter 29 Quadratic Forms. Friedrichs Extension.
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    Chapter 30 Elliptic Differential Operators
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    Chapter 31 Spectral Functions
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    Chapter 32 The Schrödinger Operator
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    Chapter 33 The Magnetic Schrödinger Operator
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    Chapter 34 Integral Operators with Weak Singularities. Integral Equations of the First and Second Kinds.
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    Chapter 35 Volterra and Singular Integral Equations
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    Chapter 36 Approximate Methods
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    Chapter 37 Introduction
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    Chapter 38 Local Existence Theory
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    Chapter 39 The Laplace Operator
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    Chapter 40 The Dirichlet and Neumann Problems
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    Chapter 41 Layer Potentials
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    Chapter 42 Elliptic Boundary Value Problems
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    Chapter 43 The Direct Scattering Problem for the Helmholtz Equation
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    Chapter 44 Some Inverse Scattering Problems for the Schrödinger Operator
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    Chapter 45 The Heat Operator
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    Chapter 46 The Wave Operator