## Almost Periodic Functions |

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### Contents

Generalisation of almost periodic | 67 |

Appendix B a p functions | 113 |

Memoirs referred to in the text | 179 |

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absolutely convergent analytic functions arbitrary Ba.p Bessel inequality Bochner-Fejer polynomial characteristic function class of u.a.p. closure conclude consider converges uniformly Corollary define definition denote differ from nought differs from zero Dirichlet series domain exists a number F(xi Fatou's Theorem finite number fortiori Fourier exponents Fourier series function f(x generalisation half-plane Hence identical inclusion interval infinite integer integral interval of length limit periodic function Parseval equation partial sums points positive integer positive number preceding theorem proof properties proves the lemma proves the theorem purely periodic functions real numbers relatively dense right-hand side satisfies the condition satisfies the inequality sequence of trigonometric set Ee set of numbers strip summation Take tend to zero theory translation number belonging trigono trigonometric polynomials trigonometric series u.a.p. function uniform almost periodicity uniformly continuous uniformly convergent upper bound vectors whence Wp a.p. function write