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Journal of the Ramanujan Mathematical Society

Volume 34, Issue 2, June 2019  pp. 185–190.

On a complex sequence of vanishing moments

Authors:  Manas R. Sahoo, Engu Satyanarayana and Abhrojyoti Sen
Author institution:School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, HBNI, P. O. Jatni, Khurda 752 050, Odisha, India

Summary:  This paper shows that vanishing of all moments of the complex sequence {zj} implies that {zj} is identically zero, provided {zj} 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.

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