7 papers
Convexity on manifolds without focal points and applications
Aprameyan Parthasarathy, B Sivashankar
In this article, we study strictly convex functions on Riemannian manifolds without focal points, a broad class of manifolds encompassing all Hadamard manifolds as well as a large…
Boundary Values of Eigenfunctions on Riemannian Symmetric Spaces
Sönke Hansen, Joachim Hilgert, Aprameyan Parthasarathy
We give a new and self-contained proof of a generic version of the (former) Helgason conjecture. It says that for generic spectral parameters the Poisson transform is a topological…
Resonances and Scattering Poles in Symmetric Spaces of Rank One
Sönke Hansen, Joachim Hilgert, Aprameyan Parthasarathy
We relate resolvent and scattering kernels for the Laplace operator on Riemannian symmetric spaces of rank one via boundary values in the sense of Kashiwara-Oshima. From this, we d…
Domains of holomorphy for irreducible admissible uniformly bounded representations of simple Lie groups
Gang Liu, Aprameyan Parthasarathy
In this note, we address a question raised by Krötz on the classification of domains of holomorphy of irreducible admissible Banach representations for connected non-compact simple…
Microlocal analysis on wonderful varieties. Regularized traces and global characters
Stephanie Cupit-Foutou, Aprameyan Parthasarathy, Pablo Ramacher
Let be a connected reductive complex algebraic group with split real form . Consider a strict wonderful -variety equipped with its -equi…
Integral operators on the Oshima compactification of a Riemannian symmetric space of non-compact type. Regularized traces and characters
Aprameyan Parthasarathy, Pablo Ramacher
Consider a Riemannian symmetric space of non-compact type, where denotes a connected, real, semi-simple Lie group with finite center, and a maximal compact subgrou…