Restriction theorems for the p-analog of the Fourier-Stieltjes algebra

2024/05/23 by Dabra, Arvish, Kumar, N. Shravan
#43A25 #43A65 #46J10 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A15 #Secondary 22D12

paper · doi:10.48550/arxiv.2405.14227

Abstract

For a locally compact group G and 1 < p < ∞, let B_p(G) denote the p-analog of the Fourier-Stieltjes algebra B(G) (or B₂(G)). Let r: B_p(G) → B_p(H) be the restriction map given by r(u) = u|_H for any closed subgroup H of G. In this article, we prove that the restriction map r is a surjective isometry for any open subgroup H of G. Further, we show that the range of the map r is dense in B_p(H) when H is either a compact normal subgroup of G or compact subgroup of an [SIN]_H-group.

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