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Abstract

We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions $g ↦ P_{g,ϕ}$, where for a fixed function ϕ, $P_{g,ϕ}$ denotes the one-dimensional orthogonal projection on the function $U_gϕ$, U is a group representation and g is an element of the group. They are defined as integrals $ʃ_W P_{g,ϕ} dg$, where W is an open, relatively compact subset of a group. Our main result is a characterization of function spaces corresponding to local Toeplitz operators with pth power summable eigenvalues, 0 < p ≤ ∞.