Cowling-Price theorem and characterization of heat kernel on symmetric   spaces
  We extend the uncertainty principle, the Cowling--Price theorem, on non-compact Riemannian symmetric spaces $X$. We establish a characterization of the heat kernel of the Laplace--Beltrami operator on $X$ from integral estimates of the Cowling--Price type. 
Swagato K Ray and Rudra P Sarkar