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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Acknowledgements
Manoj Kumar would like to thank the University Grants Commission, India (Grant no. 415846), for providing the research grant.
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Kumar, M., Kumar, N.S. Fourier analysis associated to a vector measure on a compact group. RACSAM 114, 50 (2020). https://doi.org/10.1007/s13398-019-00780-8
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DOI: https://doi.org/10.1007/s13398-019-00780-8