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Fourier Series by Gustaf Gripenberg
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**About this book :- **
**Fourier Series ** written by
** Gustaf Gripenberg **.

**Book Detail :- **
** Title: ** Fourier Series
** Edition: **
** Author(s): ** Gustaf Gripenberg
** Publisher: **
** Series: **
** Year: **
** Pages: ** 137
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: ** US
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**Book Contents :- **
**Fourier Series ** written by
** Gustaf Gripenberg **
cover the following topics.
**0. Integration theory**
**1. Finite Fourier Transform**

Introduction, L2-Theory (“Energy theory”), Convolutions (”Faltningar”), Applications, Wirtinger’s Inequality, Weierstrass Approximation Theorem, Solution of Differential Equations, Solution of Partial Differential Equations
**2. Fourier Integrals**

L1-Theory, Rapidly Decaying Test Functions, L2-Theory for Fourier Integrals, An Inversion Theorem, Applications, The Poisson Summation Formula, Is Ld1(R) = C0(R) ?, The Euler-MacLauren Summation Formula, Schwartz inequality, Heisenberg’s Uncertainty Principle, Weierstrass’ Non-Differentiable Function, Differential Equations, Heat equation, Wave equation
**3. Fourier Transforms of Distributions**

What is a Measure?, What is a Distribution?, How to Interpret a Function as a Distribution?, Calculus with Distributions, The Fourier Transform of a Distribution, The Fourier Transform of a Derivative, Convolutions (”Faltningar”), Convergence in S, Distribution Solutions of ODE:s, The Support and Spectrum of a Distribution, Trigonometric Polynomials, Singular differential equations
**4. Fourier Series**
**5. The Discrete Fourier Transform**

Definitions, FFT=the Fast Fourier Transform, Computation of the Fourier Coefficients of a Periodic Function, Trigonometric Interpolation, Generating Functions, One-Sided Sequences, The Polynomial Interpretation of a Finite Sequence, Formal Power Series and Analytic Functions, Inversion of (Formal) Power Series, Multidimensional FFT
**6. The Laplace Transform**

General Remarks, The Standard Laplace Transform, The Connection with the Fourier Transform, The Laplace Transform of a Distribution, Discrete Time: Z-transform, Using Laguerra Functions and FFT to Compute Laplace Transforms

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