The Heat Operator of a Transversally Elliptic Operator

2017/05/25 by Masahiro Morimoto, Morimoto, Masahiro
Mathematics · #58J50 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1705.09039

openalex publication_date 2017/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected compact Lie group. We study the heat operator of a G-transversally elliptic operator. After we review the spectral properties of a G-transversally elliptic operator, we define the character, that is a distribution on G generalizing the trace of the heat operator to the G-equivariant case. The main theorem of this paper gives the estimate of f_α(t), which essentially determines the convergence of the character.

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