Turkish Journal of Analysis and Number Theory
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Turkish Journal of Analysis and Number Theory. 2015, 3(1), 33-36
DOI: 10.12691/tjant-3-1-8
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Moment Problem and Inverse Cauchy Problems for Heat Equation

O. Yaremko1, N. Yaremko1, and T. Eliseeva1

1Penza State University, Penza, Russia

Pub. Date: March 02, 2015

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


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.

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

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[1]  Akhiezer, N.I., Krein, M.G. Some Questions in the Theory of Moments, Amer. Math. Soc., 1962.
[2]  Alifanov, O.M., Inverse problems of heat exchange, M, 1988, p. 279.
[3]  Arfken, G. B.; Weber, H. J. (2000), Mathematical Methods for Physicists (5th ed.), Boston, MA: Academic Press.
[4]  Bavrin, I. I., Yaremko, O. E. Transformation Operators and Boundary Value Problems in the Theory of Harmonic and Biharmonic Functions (2003) Doklady Mathematics, 68 (3), pp. 371-375.
[5]  Baker, G. A., Jr.; and Graves-Morris, P. Padé Approximants. Cambridge U.P., 1996.
[6]  Beck, J.V., Blackwell, V., Clair, C.R., Inverse Heat Conduction. Ill-Posed Problems, M, 1989, p. 312.
[7]  Chebysev, P. Sur les valeurs limites des intégrales, Journal de Mathématiques pures et appliquées, 19 ( 1874), 157-160.
[8]  Krein, M.G. and Nudelman, A.A. The Markov Moment Problem and Extermal Problems, Translations of Mathematical Monographs, Volume Fifty, Library of Congress Cataloging in Publication Data, 1977.
[9]  Lavrentev, M.M., Some ill-posed problems of mathematical physics, Novosibirsk, AN SSSR, 1962, p. 92.
[10]  Mors, F.M., Fishbah, G. Methods of theoretical physics, 1958.
[11]  Yaremko, O.E. Matrix integral Fourier transforms for problems with discontinuous coefficients and transformation operators (2007) Doklady Mathematics, 76 (12), pp. 323-325.
[12]  Yaremko, O.E. Transformation operator and boundary value problems Differential Equation. Vol.40, No. 8, 2004, pp.1149-1160.