Harmonic Analysis of Periodic  at Infinity Functions in Homogeneous Spaces

Strukova, I. I.

doi:10.15688/jvolsu1.2017.2.3

Cited by 2 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Definition 9 directly implies that F sl, ∞ (J, X) is a closed subspace of F(J, X) that is invariant under the shift operators S(t), t ∈ J. Slowly varying and periodic at infinity functions from homogeneous spaces were studied in [16].…”

Section: Definitionmentioning

confidence: 99%

On the almost periodic at infinity functions from homogeneous spaces

Баскаков¹,

Струков²,

Strukova³

2018

Issues of Analysis

View full text Add to dashboard Cite

We consider homogeneous spaces of functions defined on the real axis (or semi-axis) with values in a complex Banach space. We study the new class of almost periodic at infinity functions from homogeneous spaces. The main results of the article are connected to harmonic analysis of those functions. We give four definitions of an almost periodic at infinity function from a homogeneous space and prove them to be equivalent. We also introduce the concept of a Fourier series with slowly varying at infinity coefficients (neither necessarily constant nor necessarily having a limit at infinity). It is proved that the Fourier coefficients of almost periodic at infinity function from a homogeneous space (not necessarily continuous) can be chosen continuous. Moreover, they can be extended on C to bounded entire functions of exponential type. Besides, we prove the summability of Fourier series by the method of Bochner-Fejer. The results were received with essential use of isometric representations and Banach modules theory.

show abstract

Section: Definitionmentioning

confidence: 99%