Half-Inverse Problem for Stieltjes String
O. Martinyuk
South-Ukrainian National Pedagogical University Staroportofrankovskaya str. 26, Odessa, 65020, Ukraine.
V. Pivovarchik *
South-Ukrainian National Pedagogical University Staroportofrankovskaya str. 26, Odessa, 65020, Ukraine.
*Author to whom correspondence should be addressed.
Abstract
The Dirichlet-Robin boundary value problem generated by the Stieltjes string vibrations recurrence relations is considered. It is shown that the spectrum of this problem, the values of the point masses and of lengths of the subintervals on the left part of the string together with the total length of it and the constant in the Robin condition uniquely determine the values of point masses and of lengths of the subintervals on the right part of this Stieltjes string if the number of the point masses on the left part is the same as this number on the right part. A method of recovering the values of point masses and of lengths of the subintervals on the right part is given. Necessary and sufficient conditions of solvability of such problem are obtained.
Keywords: eigenvalue, interpolation, Hochstadt-Lieberman problem, Dirichlet condition, Robin condition, Jacobi matrix, Stieltjes function, continued fraction