On the Lebesgue constants of some classes of almost periodic functions

This paper is a study of the behavior of the Lebesgue constants of almost periodic functions of the classes $G(H)$ for which the characterizing property $H$ is a specified spacing for the spectra of the functions belonging to the class. Here $G(H)$ denotes the class of a.p. functions $f(x)$ which have the characterizing property $H$, satisfy the inequality $\sup_{-\infty<x<\infty}|f(x)|\leqslant1$, and whose Fourier exponents have a unique limit point $\Lambda^*=\infty$ or $\Lambda^*=0$.
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