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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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