Dissipative Sturm-Liouville Operators with Transmission Conditions [PDF]
Abstract and Applied Analysis, 2013 In this paper we study dissipative Sturm-Liouville operators with transmission conditions. By using Pavlov’s method (Pavlov 1947, Pavlov 1981, Pavlov 1975, and Pavlov 1977), we proved a theorem on completeness of the system of eigenvectors and associated
Hüseyin Tuna, Aytekin Eryılmaz
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Comparison and oscillation theorems for singular Sturm-Liouville operators [PDF]
Opuscula Mathematica, 2014 We prove analogues of the classical Sturm comparison and oscillation theorems for Sturm-Liouville operators on a finite interval with real-valued distributional potentials.
Monika Homa, Rostyslav Hryniv
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Spectral analysis of q-fractional Sturm-Liouville operators [PDF]
Electronic Journal of Differential Equations, 2017 In this article, we study q-fractional Sturm-Liouville operators. Using by the functional method, we pass to a new operator. Then, showing that this operator is a maximal operator and constructing a self-adjoint dilation of the maximal dissipative ...
Bilender P. Allahverdiev, Huseyin Tuna
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Electronic Journal of Differential Equations, 2017 In this article we consider a second-order Sturm-Liouville operator with a spectral parameter in the boundary condition on bounded time scales. We construct a selfadjoint dilation of the dissipative Sturm-Liouville operators.
Bilender P. Allahverdiev +2 more
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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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On the Jost Solutions of A Class of the Quadratic Pencil of the Sturm-Liouville Equation
Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2023 In this study we construct new integral representations of Jost-type solutions of the quadratic pencil of the Sturm-Liouville equation with the piece-wise constant coefficient on the entire real line.
Döndü Nurten Cücen, Anar Adiloğlu
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On non-uniqueness of recovering Sturm-Liouville operators with delay [PDF]
Communications in nonlinear science & numerical simulation, 2020 . As is known, for each fixed ν ∈ {0, 1}, the spectra of two operators generated by −y′′(x)+ q(x)y(x − a) and the boundary conditions y(ν)(0) = y(j)(π) = 0, j = 0, 1, uniquely determine the complex-valued square-integrable potential q(x) vanishing on (0,
Nebojša Djurić, S. Buterin
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Spectral analysis of discontinuous Sturm-Liouville operators with Herglotzs transmission
Electronic Research Archive, 2023 In this paper, we study the spectral properties of the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions.
Gao-Feng Du +2 more
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The Principle of Localization at the Class of Functions Integrable in the Riemann for the Processes of Lagrange - Sturm - Liouville [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 Let us say that the principle of localization holds at the class of functions $F$ at point $x_0 \in [0, \pi]$ for the Lagrange\,--\,Sturm\,--\,Liouville interpolation process $L_n^{SL}(f,x)$ if $\lim_{n \rightarrow \infty}\left|L_n^{SL}(f, x_0)-L_n^{SL ...
Aleksandr Yurievich Trynin +1 more
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Continuations of Hermitian indefinite functions and corresponding canonical systems : an example [PDF]
, 2004 M. G. Krein established a close connection between the continuation problem of positive definite functions from a finite interval to the real axis and the inverse spectral problem for differential operators.
Langer, M. +5 more
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