Spectral Barron spaces of vector-valued functions on compact groups

TL;DR

This paper explores spectral Barron spaces of vector-valued functions on compact groups, focusing on their properties and relationships with other function spaces like Sobolev and bounded function spaces.

Contribution

It introduces and analyzes spectral Barron spaces for vector-valued functions on compact groups, highlighting their functional properties and embeddings.

Findings

Characterization of spectral Barron spaces with summability Fourier transform properties

Continuous embeddings into Sobolev and bounded function spaces established

Insights into the structure and properties of vector-valued function spaces on compact groups

Abstract

In this article, we study spectral Barron spaces whose elements are made up of some vector-valued functions on a compact group whose Fourier transforms admit a certain summability property. We investigate their functional properties and some continuous embeddings of these spaces with respect to other function spaces among which are Sobolev spaces of vector-valued functions and the space of bounded vector-valued functions on compact groups.