Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Yurko V. A. Recovering Differential Operators on a Graph with a Cycle and with Generalized Matching Conditions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2008, vol. 8, iss. 3, pp. 10-17. DOI: 10.18500/1816-9791-2008-8-3-10-17

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
16.06.2008
Full text:
(downloads: 156)
Language: 
Russian
Heading: 
UDC: 
517.984

Recovering Differential Operators on a Graph with a Cycle and with Generalized Matching Conditions

Autors: 
Yurko Vjacheslav Anatol'evich, Saratov State University
Abstract: 

The solution of the inverse spectral problem is obtained for second-order differential operators on a graph with a cycle and with generalized matching conditions in the internal vertex.

Key words: 
References: 
  1. Марченко В.А. Операторы Штурма – Лиувилля и их приложения. Киев: Наук. думка, 1977.
  2. Левитан Б.М. Обратные задачи Штурма – Лиувилля. М.: Наука, 1984.
  3. Beals R., Deift P., Tomei C. Direct and Inverse Scattering on the Line, Math. Surveys and Monographs. V.28. Amer. Math. Soc. Providence: RI, 1988.
  4. Freiling G., Yurko V.A. Inverse Sturm – Liouville Problems and their Applications. N.Y.: NOVA Science Publishers, 2001.
  5. Yurko V.A. Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series. Utrecht: VSP, 2002.
  6. Юрко В.А. Введение в теорию обратных спектральных задач. М.: Физматлит, 2007.
  7. Покорный Ю.В., Пенкин О.М., Прядиев В.Л. и др. Дифференциальные уравнения на геометрических графах. М.: Физматлит, 2004.
  8. Yurko V.A. Inverse spectral problems for Sturm –Liouville operators on graphs // Inverse Problems. 2005. V. 21. P. 1075–1086.
  9. Naimark M.A. Linear Differential Operators, 2nd ed., M.: Nauka, 1969; English transl. of 1st ed. P. I, II. N.Y.: Ungar, 1967, 1968.
  10. Bellmann R., Cooke K. Differential-difference Equations. N.Y.: Academic Press, 1963.
  11. Conway J.B. Functions of One Complex Variable, 2nd ed. V. I. N.Y.: Springer-Verlag, 1995.
  12. Станкевич И.В. Об одной обратной задаче спектрального анализа для уравнения Хилла // Докл. АН СССР. 1970. Т. 192, No 1. С. 34–37.
  13. Марченко В.А., Островский И.В. Характеристика спектра оператора Хилла // Мат. сб. 1975. Т. 97. С. 540–606.