2011/02/24 by Aprameyan Parthasarathy, Parthasarathy, Aprameyan, Pablo Ramacher +1
Mathematics · #22E46 #32J05 #47A10 #53C35 #58J35 #58J37 #58J40 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #math.DG #msc:22E46 #msc:32J05 #msc:47A10 #msc:53C35 #msc:58J35 #msc:58J37 #msc:58J40
paper · pdf · doi:10.48550/arxiv.1102.5069
26 pages
arxiv created 2011/02/24 · openalex publication_date 2011/02/24 · arxiv updated 2011/02/25 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Let \X≃ G/K be a Riemannian symmetric space of non-compact type, \widetilde \X its Oshima compactification, and (π,C(\widetilde \X)) the regular representation of G on \widetilde \X. We study integral operators on \widetilde \X of the form π(f), where f is a rapidly falling function on G, and characterize them within the framework of pseudodifferential operators, describing the singular nature of their kernels. In particular, we consider the holomorphic semigroup generated by a strongly elliptic operator associated to the representation π, as well as its resolvent, and describe the asymptotic behavior of the corresponding semigroup and resolvent kernels.