Moment Problem and Inverse Cauchy Problems for Heat Equation

O. Yaremko¹, N. Yaremko^1, and T. Eliseeva¹

¹Penza State University, Penza, Russia

Cite this paper:
O. Yaremko, N. Yaremko and 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

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.

Keywords:
hamburger and stieltjes moment problem inverse cauchy problem hermite polynomials poisson integral

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