## Fourier series and integrals |

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### Contents

Fourier Integrals | 86 |

Fourier Integrals and Complex Function Theory | 144 |

Fourier Series and Integrals on Groups | 203 |

Copyright | |

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### Common terms and phrases

action of G analytic application approximated band-limited functions bounded Cauchy's formula character circle complex numbers compute constant multiple converges defined differential operator double coset eigenfunctions eigenvalue evaluation example EXERCISE 12 EXERCISE 9 exponential type expressed fact finish the proof finite fixed form a unit-perpendicular Fourier integral Fourier series Fourier transform function fe functions of class group G half-plane Hardy function harmonic of weight heat flow Heisenberg's inequality Hilbert space Hint homomorphism indicator function inner product interval inversion formula isomorphic JG JG lattice Lebesgue integral lemma means measurable modulo nfoo nonnegative perpendicular pick Plancherel identity plane Poisson summation formula pole polynomial prime problem proof is finished prove recipe Riemann Riemann-Lebesgue lemma rotation Section self-evident solution span spherical function spherical harmonics Step subgroup Subsection summable function theorem unit-perpendicular basis unit-perpendicular family vanishes verify