Uniform subalgebras of $L^{\infty }$ on the unit circle generated by almost periodic functions

On Uniform Subalgebras of L∞ on the Unit Circle Generated by Almost Periodic Functions

In the present paper we introduce analogs of almost periodic functions on the unit circle. We study certain uniform algebras generated by such functions, prove corona theorems for them and describe their maximal ideal spaces. 1. Formulation of Main Results 1.1. The classical almost periodic functions on the real line first introduced by H. Bohr in the 1920s play an important role in various are...

Uniform Subalgebras of L∞ on the Unit Circle Generated by Almost Periodic Functions

Analogs of almost periodic functions for the unit circle are introduced. Certain uniform algebras generated by such functions are studied, the corona theorems for them are proved, and their maximal ideal spaces are described. §1. Formulation of main results 1.1. The classical almost periodic functions on the real line, as first introduced by H. Bohr in the 1920s, play an important role in vario...

On Hartman Almost Periodic Functions

In this note we consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in R or Z. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally co...

Almost periodic functions, constructively

Almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr’s fundamental theorem for almost periodic functions which we then generalize to almost periodic functions on general topological groups.

On the Derivatives of Functions Analytic in the Unit Circle.