Abstract
To solve the inverse problem for the Sturm-Liouville operator with eigenvalue parameter dependent boundary conditions we reconstruct the spectral distribution function from two spectra of the boundary-value problems with equal Θ(λ) and different real constants in the boundary conditions. The well-known results of A.V. Strauss [5] concerning the connection between the eigenvalue problems with the spectral parameter in the boundary conditions and the theory of generalized resolvents is used.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Krein M.G. On some cases of effective determination of the density of a non-homogeneous string by its spectral function. Dokl.Akad.Nauk SSSR, (1953), 93, N4, 617–620.
M.G. Krein, On inverse problems for inhomogeneous strings, Dokl. Akad. Nauk SSSR, 82 (1952), 669–672.
I.M. Gel’fand and B.M. Levitan, On a simple identity for the characteristic values of a differential operator of the second order, Dokl. Akad. Nauk SSSR, 88 (1953), 593–596.
Strauss A.V. On selfadjoint operators acting in the orthogonal sum of Hilbert spaces. Dokl. Akad. Nauk SSSR, (1962), 144, N3, 512–515.
A.V. Strauss, On the spectral functions of differential operators, Izv. Akad. Nauk SSSR, Ser. Mat., 19 (1955), 201–220.
M.V. Chugunova, On the inverse spectral problem for the finite interval, Funct. Analysis, Ulyanovsk, 35 (1994), 113–123.
M.V. Chugunova, On the effective methods for the solution of some inverse problems, Funct. Analysis, Ulyanovsk, 36 (1997), 66–75.
N. Aronszajn, W.F. Donoghue, On the exponential representations of analytic functions in the upper half-plane with positive imaginary part, J. d’Analyse Math., 5 (1956), 321–388.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Chugunova, M.V. (2001). Inverse Spectral problem for the Sturm-Liouville Operator with Eigenvalue Parameter Dependent Boundary Conditions. In: Alpay, D., Vinnikov, V. (eds) Operator Theory, System Theory and Related Topics. Operator Theory: Advances and Applications, vol 123. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8247-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8247-7_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9491-3
Online ISBN: 978-3-0348-8247-7
eBook Packages: Springer Book Archive