Let G a free group with r generators. In this paper we consider an analytic family of representations π_z, z=s+it ∈ C on Hilbert spaces H_s. We explicitly compute constants c(s,t) such that ||π_z(x)f|| ≤ c(s,t) ||f||_s for all f ∈ H_s, x ∈ G. From the properties of these constants we deduce a density theorem for multipliers on L^p(G).
Uniformly bounded representations and L^p-convolution operators on a free group
MANTERO, ANNA MARIA;ZAPPA, ANNA
1983-01-01
Abstract
Let G a free group with r generators. In this paper we consider an analytic family of representations π_z, z=s+it ∈ C on Hilbert spaces H_s. We explicitly compute constants c(s,t) such that ||π_z(x)f|| ≤ c(s,t) ||f||_s for all f ∈ H_s, x ∈ G. From the properties of these constants we deduce a density theorem for multipliers on L^p(G).
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