Theorems of Chernoff and Ingham for certain eigenfunction expansions

2020/11/19 by Ganguly, Pritam, Thangavelu, Sundaram
#35P10 #42C05. Secondary: 33C45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 43A85

paper · doi:10.48550/arxiv.2011.09940

Abstract

We prove an uncertainty principle for certain eigenfunction expansions on L²(ℝ⁺,w(r)dr) and use it to prove analogues of theorems of Chernoff and Ingham for Laplace-Beltrami operators on compact symmetric spaces, special Hermite operator on ℂⁿ and Hermite operator on ℝⁿ.

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