The Hochstadt-Lieberman theorem for Stieltjes string (in Ukrainian) |
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| Author |
martynyuk_olga@mail.ru
K. D. Ushinsky South Ukrainian State Pedagogical University
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| Abstract |
The following problem is considered. The values of point masses located on the left part of a Stieltjes string are known together with the lengths of the intervals between them. The number of the masses on the left part is the half of the total number of masses. The spectrum of the Dirichlet problem is also known as well as the the total length of the string. The values of the masses on the right part and the lengths of the intervals between them should be found. A necessary and sufficient condition for existence of a solution of such problem is given in an implicit form. It is proved that the solution is unique. A method of recovering values of the masses and lengths of the intervals on the right part is proposed.
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| Keywords |
Stieltjes string, spectrum of Dirichlet problem, implicit form, point mass
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| DOI |
doi:10.30970/ms.34.1.80-89
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Reference |
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| Pages |
80-89
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| Volume |
34
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| Issue |
1
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| Year |
2010
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |