## Fourier Series and IntegralsThe ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text. |

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### Contents

Fourier Series | 5 |

Fourier Integrals | 86 |

Fourier Integrals and Complex Function Theory | 144 |

Copyright | |

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### Common terms and phrases

actually addition analytic application approximated belongs bounded character Check circle closed coefficients complex compute constant converges coset defined differential directed easy eigenfunctions equal evaluation example EXERCISE expanded expressed fact FIGURE fixed formal formula Fourier integral Fourier series function f Hardy Hint identified identity important indicator inequality infinitely interval inverse isomorphic length less limit look means measurable modulus nf oo operator period perpendicular pick Plancherel identity plane polynomial positive present prime problem proof is finished prove recipe roots rotation sense Show side simple solution space span spherical function spherical harmonics Step Subsection summable functions tends theorem Think unit unit-perpendicular vanishes verify whole