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Integral operators on the Oshima compactification of a Riemannian symmetric space
, Ramacher Pablo
Published in Elsevier BV
Volume: 267
Issue: 4
Pages: 919 - 962

Consider a Riemannian symmetric space of non-compact type, where G is a connected, real, semisimple Lie group, and K a maximal compact subgroup. Let be its Oshima compactification, and the left-regular representation of G on . In this paper, we examine the convolution operators for rapidly decaying functions f on G, and characterize them within the framework of totally characteristic pseudodifferential operators, describing the singular nature of their kernels. As a consequence, we obtain asymptotics for heat and resolvent kernels associated to strongly elliptic operators on . As a further application, a regularized trace for the operators can be defined, yielding a distribution on G which can be interpreted as a global character of π, and is given by a fixed point formula analogous to the Atiyah–Bott character formula for an induced representation of G.

About the journal
JournalData powered by TypesetJournal of Functional Analysis
PublisherData powered by TypesetElsevier BV
Open AccessNo