Journal of the Ramanujan Mathematical Society

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On a Complex Sequence of Vanishing Moments


Affiliations
1 School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, HBNI, P. O. Jatni, Khurda 752050, Odisha, India
2 Department of Mathematical and computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India
     

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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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  • Andrew Lenard, A nonzero complex sequence with vanishing power sums, Proc. Amer. Math. Soc., 108 (1990) 951–953.

  • W. M. Priestley, Complex sequences whose “moments” all vanish, Proc. Amer. Math. Soc., 116 (1992) 437–444.


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  • On a Complex Sequence of Vanishing Moments

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Authors

Manas R. Sahoo
School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, HBNI, P. O. Jatni, Khurda 752050, Odisha, India
Engu Satyanarayana
Department of Mathematical and computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India
Abhrojyoti Sen
School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, HBNI, P. O. Jatni, Khurda 752050, Odisha, India

Abstract


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.

References