Year: 2025
Type: preprint
Abstract: Let $G$ be a locally compact second countable groupoid with a fixed Haar system $λ=\{λ^{u}\}_{u\in G^{0}}$ and $(Φ,Ψ)$ be a complementary pair of $N$-functions satisfying $Δ_{2}$-condition. In this article, we introduce the continuous field of Orlicz space $(L^Φ_{0},Δ_{1})$ and provide a sufficient condition for the space of continuous sections vanishing at infinity, denoted $E^Φ_{0}$, to be an Banach algebra under a suitable convolution. Further, the condition for a closed $C_{b}(G^{0})$-submodule $I$ of $E^Φ_{0}$ to be a left ideal is established. Moreover, we provide a groupoid analogue of the characterization of the space of convolutors of Morse-Transue space for locally compact groups.
Source: arXiv (Cornell University)
Authors: Sridharan, K. N., Kumar, N. Shravan
Institution: Indian Institute of Technology Delhi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406317698