Entire functions of exponential type, almost periodic in Besicovitch's sense on the real hyperplane

TL;DR

This paper investigates the spectral properties of almost periodic functions in Besicovitch's sense that are restrictions of entire functions of exponential type, establishing that their spectrum is contained within a specific bounded region.

Contribution

It proves that the spectrum of such almost periodic functions is confined within a ball of radius equal to the exponential type, linking spectral properties to the function's exponential growth.

Findings

Spectrum is contained within a ball of radius b centered at the origin.

Restrictions of entire functions of exponential type are almost periodic in Besicovitch's sense.

Spectral containment relates exponential type to spectral bounds.

Abstract

Suppose that an almost periodic in Besicovitch's sense function $f(x)$ of several variables is the restriction to the real hyperplane of an entire function of exponential type $b$. Then its spectrum is contained in the ball of radius $b$ with the center in the origin.