## The theory of Fourier series and integralsA concise treatment of Fourier series and integrals, with particular emphasis on their relation and importance to science and engineering. Illustrates interesting applications which those with limited mathematical knowledge can execute. Key concepts are supported by examples and exercises at the end of each chapter. Includes background on elementary analysis, a comprehensive bibliography, and a guide to further reading for readers who want to pursue the subject in greater depth. |

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### Contents

Convergence Theory | 29 |

The Dirichlet Problem and the Poisson Integral | 53 |

Conjugate Functions and Conjugate Series | 89 |

Copyright | |

5 other sections not shown

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27t-periodic FC-function absolutely convergent apply argument boundary values bounded interval Cauchy-Riemann equations chapter complex numbers complex-valued function condition consider constant continuous function convolution Corollary deduce Definition A.9 denote differentiable Dirichlet problem discontinuities divergent equal Example exercise exists exponential f(reie FC-function finite number flow formula Fourier coefficients Fourier integral Fourier series Fourier theory Fourier transform given gives harmonic conjugate harmonic function Hence hypotheses inversion Let f(x limit Lipschitz continuous notation Notice nx dx obtain orthogonal P-summable partial sums particular point of continuity Poisson integral Poisson kernel positive proof of Theorem properties prove putting reader real line real number real values reie respectively result follows Riemann-Lebesgue lemma satisfy sequence of functions series and integrals solution subinterval summability suppose tends to zero Theorem 2.3 trigonometric polynomial trigonometric systems uniform uniformly continuous uniformly convergent unit circle write