Fourier analysis associated to a vector measure on a compact group

2019/05/29 by Kumar, Manoj, Kumar, N. Shravan
#43A15 #43A30 #43A77 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1905.12209

Abstract

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.

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