Vol. 70, No. 1, 1977

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The theory of almost periodic functions in constructive mathematics

James Dennis Brom

Vol. 70 (1977), No. 1, 67–81

In this paper we develop a constructive theory of continuous almost periodic functions. We expose those aspects of the standard theory that are not constructive and give constructive substitutes. For example, it is not true in constructive mathematics that each trigonometric polynomial is almost periodic. A trigonometric polynomial is almost periodic if and only if its exponents are rationally discrete. We obtain a constructive proof of Bohr’s fundamental theorem that leads to a computational method for uniform approximations to continuous almost periodic functions by trigonometric polynomials.

Mathematical Subject Classification
Primary: 02E05, 02E05
Secondary: 42A84
Received: 13 October 1976
Published: 1 May 1977
James Dennis Brom