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An Inverse Spectral Problem for Sturm – Liouville Operators with Singular Potentials on Graphs with a Cycle [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2019 This paper is devoted to the solution of inverse spectral problems for Sturm – Liouville operators with singular potentials from class W2−1 on graphs with a cycle.
Vasilev, Sergei V.
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Linear Algebra and its Applications, 1975 AbstractIn this article an infinite periodic Jacobi matrix is under consideration. It is shown that the spectrum of the matrix consists of a single finite interval if and only if the period of the matrix is equal to unity.
Cheung, Shiu Ming, Hochstadt, Harry
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Indefinite Hamiltonian systems whose Titchmarsh–Weyl coefficients have no finite generalized poles of non-positive type [PDF]
, 2013 The two-dimensional Hamiltonian system (*) y'(x)=zJH(x)y(x), x∈(a,b), where the Hamiltonian H takes non-negative 2x2-matrices as values, and $J:= \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$, has attracted a lot of interest over the past decades ...
Harald Woracek +3 more
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Inverse Steklov Spectral Problem for Curvilinear Polygons [PDF]
International Mathematics Research Notices, 2020 Abstract This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi $, we prove that the asymptotics of Steklov eigenvalues obtained in [ 20] determines, in a constructive manner, the number of vertices and the properly ordered sequence of side lengths, as
Krymski, S +4 more
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, 2020 We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we focus on Love waves. Under certain generic conditions, we establish uniqueness and present a reconstruction scheme for the S-wavespeed with multiple ...
de Hoop, Maarten, V, +7 more
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Spectral analysis of infinite Marchenko-Slavin matrices [PDF]
Opuscula MathematicaThis work tackles the problem of spectral characterization of a class of infinite matrices arising from the modeling of small oscillations in a system of interacting particles.
Sergio Palafox, Luis O. Silva
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Inverse Sturm–Liouville Problem with Spectral Parameter in the Boundary Conditions
Mathematics, 2023 In this paper, for the first time, we study the inverse Sturm–Liouville problem with polynomials of the spectral parameter in the first boundary condition and with entire analytic functions in the second one.
Natalia P. Bondarenko, Egor E. Chitorkin
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Well-posed inverse spectral problems [PDF]
Proceedings of the National Academy of Sciences, 1975 It is known that if complete spectral data are provided, the potential function in a Sturm-Liouville operator is uniquely determined almost everywhere. If two such operators have spectra that differ in a finite number of eigenvalues, then the corresponding potential functions will no longer be the same. However, as is demonstrated when the nonidentical
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, 2020 We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [5] to Rayleigh waves.
de Hoop, Maarten, V, +7 more
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Determination of the Impulsive Dirac Systems from a Set of Eigenvalues
Mathematics, 2023 In this work, we consider the inverse spectral problem for the impulsive Dirac systems on (0,π) with the jump condition at the point π2. We conclude that the matrix potential Q(x) on the whole interval can be uniquely determined by a set of eigenvalues ...
Ran Zhang, Chuanfu Yang, Kai Wang
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