Fourier decompositions with positive coefficients in compact Gel′fand pairs

Blank, Brian E.

doi:10.1090/S0002-9939-1993-1195713-7

Fourier decompositions with positive coefficients in compact Gel′fand pairs
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by Brian E. Blank

Proc. Amer. Math. Soc. 119 (1993), 427-430

DOI: https://doi.org/10.1090/S0002-9939-1993-1195713-7

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Abstract:

For $G$ a compact separable Hausdorff topological group and for $1 < p \leqslant 2$ the finiteness of the Hausdorff-Young sequence operator is established for functions in ${L^1}(G)$ with positive Fourier decompositions and which are $p$th-power integrable in a neighborhood of the identity. A similar result is established in the context of compact Gelfand pairs.

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