Modern Analysis and Applications pp 273-289 | Cite as

# On a Moment Problem on a Curve Connected with Ill-posed Boundary Value Problems for a PDE and Some Other Problems

Chapter

## Abstract

This paper is devoted to a connection between ill-posed boundary value problems in a bounded domain for a PDE that isn’t proper elliptic and a new moment problem on a curve that is a generalization of well-known trigonometric moment problem. Some connections with another field of mathematics are given in partial cases of the curve and the equation.

## Keywords

Dirichlet Problem Periodic Point Neumann Problem Moment Problem String Equation
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## References

- [1]Yu.M. Berezanskii,
*Decomposition on eigenfunctions of self-ajoint operators*. — Kiev: Naukova dumka, 1965. (In Russian)Google Scholar - [2]V.P. Burskii,
*Boundary properties of*L_{2}-solutions*of linear differential equations and duality equation-domain*. Doclady Academii Nauk SSSR**309**(1989), no. 5, 1036–1039. (In Russian)Google Scholar - [3]V.P. Burskii,
*On boundary value problems for differential equations with constant coefficients in a plane domain and a moment problem*. Ukr. Math. Journal**48**(1993), no. 11, 1659–1668.CrossRefMathSciNetGoogle Scholar - [4]V.P. Burskii,
*Investigation methods of boundary value problems for general differential equations*. Kiev, Naukova dumka, 2002. (In Russian)Google Scholar - [5]V.P. Burskii, A.S. Zhedanov
*On Dirichlet problem for string equation, Poncelet problem, Pell-Abel equation, and some other related problems*. Ukr. Math. Journal**58**(2006), no. 4, 487–504.CrossRefMathSciNetGoogle Scholar - [6]V.P. Burskii, A.S. Zhedanov,
*Dirichlet problem for string equation, Poncelet problem and Pell-Abel equation*. Symmetry, Integrability and Geometry: Methods and Applications. 4p. arXiv:math.AP/0604278 — Apr 2006.Google Scholar - [7]M.G. Krein,
*Theory of selfadjoint expansions of semibounded Hermitian operators and its applications.*I. — Mathematical Sbornik**20**:3 (1947), 431–495. (In Russian)MathSciNetGoogle Scholar - [8]V.A. Malyshev,
*Abel equation*, Algebra and analysis**13**(2001), no. 6, 1–55. (In Russian)MathSciNetGoogle Scholar - [9]Ya.A. Roitberg,
*On boundary values of generalized solutions of elliptic systems by Duglis-Nirenberg*.**18**(1977), no. 4, 845–860. (In Russian)MathSciNetGoogle Scholar - [10]L.M. Sodin, P.M. Yuditskii,
*Functions least deviating from zero on closed sets of real axis*. Algebra and analysis**4**, no. 2, 1–61. (In Russian)Google Scholar - [11]M.Yo. Vishik,
*On general boundary value problems for elliptic differential equations*. Trudy Moskowskogo Mathematicheskogo Obshchestva**1**(1952), 187–246. (In Russian)MATHGoogle Scholar - [12]J.L. Treves,
*Lectures on linear partial differential equations with constant coefficients*. Rio de Janeiro: Instituto de Mathematica, 1961.MATHGoogle Scholar

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