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Asymptotic Expansion for Expanding Spherical Averages in Real Rank One

Representation Theory 2026-01-30 v1

Abstract

This paper develops precise asymptotic formulas for expanding non-spherical averages on compact quotients of real rank-one Lie groups, focusing on SO(n,1)SO(n,1) as a model case. Using tools from harmonic analysis and representation theory, the study reduces the analysis of orbit averages to an ordinary (ODE) derived from the action of the Casimir operator.

Keywords

Cite

@article{arxiv.2601.21954,
  title  = {Asymptotic Expansion for Expanding Spherical Averages in Real Rank One},
  author = {Zhiyuan Deng and Yutian Sun},
  journal= {arXiv preprint arXiv:2601.21954},
  year   = {2026}
}