MATHEMATICA BOHEMICA, Vol. 121, No. 3, pp. 249-262, 1996

Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions

Alexandr Fischer

Alexandr Fischer, Czech Technical University, Faculty of Mechanical Engineering, Dept. of Technical Mathematics, Karlovo nam. 13, 121 35 Praha 2, Czech Republic

Abstract: The paper deals with almost periodic functions which are limits of sequences of continuous periodic functions, and determines the structure of their Fourier exponents and their ranges. It is shown that the class $CP(\X)$ of continuous periodic functions is not densely distributed in the space $AP(\X)$.

Keywords: almost periodicity (Bohr), Fourier coefficient, Fourier exponent, Bochner transformation

Classification (MSC 1991): 42A75

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