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arXiv · 1905.12209

Fourier analysis associated to a vector measure on a compact group

Manoj Kumar·N. Shravan Kumar
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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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Manoj Kumar, N. Shravan Kumar. 2019-05-29. Fourier analysis associated to a vector measure on a compact group. https://arxiv.org/abs/1905.12209

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