Abstract
Let Γ be a discrete subgroup of PSL(2,ℝ) of infinite covolume with infinite conjugacy classes. H t denotes the Hilbert space consisting of analytic functions in \({L^2}(\mathbb{D},{({\text{Im }}z)^{t-2}}{\text{d}}\bar z{\text{d}}z)\) and, for t > 1, π t denotes the corresponding projective unitary representation of PSL(2, ℝ) on this Hilbert space. Let A t be the II∞ factor given by the commutant of π t(Γ) in B(H t). Let F denote a fundamental domain for Γ in D. We assume that t > 5 and give \(partial M = \partial \mathbb{D} \cap \bar F\) the topology of disjoint union of its connected components.
Keywords
Toeplitz Operator Boundary Component Fundamental Domain Discrete Subgroup Trace Class
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