## Fourier series: a modern introduction, Volume 1 |

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### Contents

TRIGONOMETRIC SERIES | 1 |

GROUP STRUCTURE | 14 |

CONVOLUTIONS OF FUNCTIONS | 50 |

Copyright | |

9 other sections not shown

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Abelian groups absolutely continuous appear Appendix apply approximate identity assertion assume Banach space bounded variation Chapter 12 compact Abelian groups complex numbers complex-valued functions continuous functions continuous linear converges almost everywhere deduce defined denote diverge dual everywhere dense example Exercise exists finitely follows Fourier series Frechet space functions f g e L1 given group algebra harmonic analysis Hint homomorphism integrable functions interval invariant integral Kah2 Lebesgue lim sup linear functional linear subspace locally compact mapping metric neighborhood nonmeager nonnegative norm notation orthogonality relations Parseval formula partial sums periodic function points pointwise convergence pointwise representation positive definite functions positive numbers problem proof Prove reader real numbers real-valued Remarks satisfying Section seminorms sequence subset sufficient Suppose theory topological group topological linear space trigonometric polynomials trigonometric series uniform boundedness principle uniformly convergent verify zero