arXiv subjects

N. Shravan Kumar

Publications and source records attributed to N. Shravan Kumar.

23 records · Page 2Linked to original sources

arXiv2019

Weakly Almost Periodic and Uniformly continuous functionals on the Orlicz Figa Talamanca Herz algebras

In this paper we study weakly almost periodic and uniformly continuous functionals on the Orlicz Figà-Talamanca Herz algebras associated to a locally compact group. We show that a unique invariant mean exists on the space of weakly almost periodic functionals. We also characterise discrete groups in terms of the inclusion of the space of uniformly continuous functions inside the space of weakly almost periodic functionals.

math.FA↗

arXiv2019

Optimal extension of the Fourier transform and convolution operator on compact groups

Let $G$ be a compact group (not necessarily abelian) and let $Φ$ be a Young function satisfying the $Δ_2$-condition. We determine the optimal domain and the associated extended operator for both Fourier transform and the convolution operator defined on the Orlicz spaces $L^Φ(G).$

math.FA↗

arXiv2019

Fourier analysis associated to a vector measure on a compact group

In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also introduce and study the convolution of functions from $L^p$-spaces associated to a vector measure. We prove some analogues of the classical Young's inequalities. Similarly, we also study convolution of a scalar measure and a vector measure.

math.FA↗

arXiv2019

Convolution structures for an Orlicz space with respect to vector measures on a compact group

The aim of this paper is to present some results about the space L^Φ(ν), where νis a vector measure on a compact (not necessarily abelian) group and Φis a Young function. We show that under certain conditions, the space L^Φ(ν) becomes an L^1(G)-module with respect to the usual convolution of functions. We also define one more convolution structure on L^Φ(ν).

math.FA↗

arXiv2019

Representations of the Orlicz Figa-Talamanca Herz Algebras and Spectral subspaces

Let G be a locally compact group. In this note, we characterise non-degenerate *-representations of A_Φ(G) and B_Φ(G). We also study spectral subspaces associated to a non-degenerate Banach space representation of A_Φ(G).

math.FA↗