On a complex sequence of vanishing moments

Abstract

This paper shows that vanishing of all moments of the complex sequence {z<inf>j</inf>} implies that {z<inf>j</inf>} is identically zero, provided {z<inf>j</inf>} is in lp,1 ? p < ?. This proof is different from one given by Priestley [Proc. Amer. Math. Soc. 116 (1992) 437–444] and shows an interesting connection of this problem with heat kernel. © 2019 Ramanujan Mathematical Society. All rights reserved.