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Lavrentev, M.M., Some ill-posed problems of mathematical physics, Novosibirsk, AN SSSR, 1962, p. 92.

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Article

Moment Problem and Inverse Cauchy Problems for Heat Equation

1Penza State University, Penza, Russia


Turkish Journal of Analysis and Number Theory. 2015, Vol. 3 No. 1, 33-36
DOI: 10.12691/tjant-3-1-8
Copyright © 2015 Science and Education Publishing

Cite this paper:
O. Yaremko, N. Yaremko, T. Eliseeva. Moment Problem and Inverse Cauchy Problems for Heat Equation. Turkish Journal of Analysis and Number Theory. 2015; 3(1):33-36. doi: 10.12691/tjant-3-1-8.

Correspondence to: N.  Yaremko, Penza State University, Penza, Russia. Email: yaremki@mail.ru

Abstract

The solution of Hamburger and Stieltjes moment problem can be thought of as the solution of a certain inverse Cauchy problem. The solution of the inverse Cauchy problem for heat equation is founded in the form of Hermite polynomial series. The author reveals, the formulas obtained by him for the solution of inverse Cauchy problem have a symmetry with respect to the formulas for corresponding direct Cauchy problem. Obtained formulas for solution of the inverse problems can serve as a basis for the solution of the moment problem.

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