Heat kernel and Hardy's theorem for Jacobi transform (Q1431018)

The authors first obtain sharp upper and lower bounds for the heat kernel associated with the Jacobi transform. The authors then use this sharp estimates of the heat kernel and a lemma of \textit{A. Sitaram} and \textit{M. Sundari} [Pac. J. Math. 177, 187--200 (1997; Zbl 0882.43005)] to establish some analogues of Hardy's theorem for the Jacobi transform, namely that \(f\) and its Jacobi transform \(\widehat f\) cannot both be ``very rapidly decreasing''.