Almost periodic functions

Introduction. Periodic functions, Fourier series Almost Periodic Functions: 1 Definitions and fundamental properties 2 Two characteristic properties of almost periodic functions 3 The Fourier series associated with an almost periodic function 4 Convergence of Fourier series 5 Summability of Fourier series 6 Almost periodic numeric sequences and their connection with almost periodic functions Bibliographical notes Almost Periodic Functions Depending on Parameters: 1 Almost periodic functions depending uniformly on parameters 2 Almost periodic functions in the mean 3 Random functions almost periodic in probability Analytic Almost Periodic Functions: 1 Preliminary theorems 2 Elementary properties of analytic almost periodic functions 3 The Dirichlet series associated with an analytic almost periodic function 4 The behavior at infinity of analytic almost periodic functions in a half-plane Bibliographical notes Almost Periodic Solutions of Ordinary Differential Equations: 1 The primitive of an almost periodic function 2 Linear systems with constants coefficients 3 Quasilinear systems 4 An Amerio criterion for almost periodicity of bounded solutions 5 The equation of non-linear oscillations Bibliographical notes Almost Periodic Solutions of Partial Differential Equations: 1 Some properties of harmonic and polyharmonic functions 2 Harmonic and polyharmonic almost periodic functions 3 Almost periodic solutions of hyperbolic equations 4 Almost periodic solutions of certain parabolic equations Bibliographical notes Almost Periodic Functions with Values in Banach Spaces: 1 Definitions and general properties 2 The Banach space of almost periodic functions 3 The Fourier series attached to an almost periodic function with values in a Banach space. The approximation theorem 4 Almost periodic functions in the Muckenhoupt sense and in the Stepanov sense 5 Weakly almost periodic functions. The primitive of an almost periodic function Bibliographical notes Almost Periodic Functions on Groups: 1 Elementary properties of almost periodic functions on groups. The existence of the mean 2 Unitary representations of groups. The Fourier series associated with an almost periodic function 3 The uniqueness and approximation theorems 4 Almost periodic functions on topological groups Bibliographical notes Appendix References Index.