Results 11 to 20 of about 10,340 (200)
Transformation Operators for Sturm-Liouville Operators with Singular Potentials [PDF]
Mathematical Physics, Analysis and Geometry, 2004 Transformation operators are constructed for the Sturm-Liouville operator \(\ell f:=f''+qf\) with a singular complex-valued potential \(q\in W_2^{-1}(0,1)\). Some applications to the spectral analysis of Sturm-Liouville operators with singular potentials are also given.
Hryniv, Rostyslav O. +1 more
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Relative oscillation theory for Sturm–Liouville operators extended
Journal of Functional Analysis, 2008 We extend relative oscillation theory to the case of Sturm--Liouville operators $H u = r^{-1}(-(pu')'+q u)$ with different $p$'s. We show that the weighted number of zeros of Wronskians of certain solutions equals the value of Krein's spectral shift function inside essential spectral gaps.
Krüger, Helge, Teschl, Gerald
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Sturm–Liouville operator functions [PDF]
Dissertationes Mathematicae, 2018 Summary: Many special functions are solutions of both a differential and a functional equation. We use this duality to solve a large class of abstract Sturm-Liouville equations on the non-negative real line, initiating a theory of Sturm-Liouville operator functions; cosine, Bessel, and Legendre operator functions are special cases.
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Inverse eigenvalue problems for rank one perturbations of the Sturm-Liouville operator
Open Mathematics, 2022 This article is concerned with the inverse eigenvalue problem for rank one perturbations of the Sturm-Liouville operator. I obtain the relationship between the spectra of the Sturm-Liouville operator and its rank one perturbations, and from the spectra I
Wu Xuewen
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Sturm-Liouville Operators [PDF]
, 2020 Second-order Sturm-Liouville differential expressions generate self-adjoint differential operators in weighted L2-spaces on an interval (a, b).
Jussi Behrndt, Seppo Hassi, Henk De Snoo
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Қарағанды университетінің хабаршысы. Математика сериясы, 2020 It is known that the eigenvalues λn(n = 1, 2, ...) numbered in decreasing order and taking the multiplicity of the self-adjoint Sturm-Liouville operator with a completely continuous inverse operator L−1 have the following property (∗) λn → 0, when n → ∞,
M.B. Muratbekov, M.M. Muratbekov
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Transformation operators for impedance Sturm–Liouville operators on the line
Математичні Студії, 2023 In the Hilbert space $H:=L_2(\mathbb{R})$, we consider the impedance Sturm--Liouville operator $T:H\to H$ generated by the differential expression $ -p\frac{d}{dx}{\frac1{p^2}}\frac{d}{dx}p$, where the function $p:\mathbb{R}\to\mathbb{R}_+$ is of ...
M. Kazanivskiy +2 more
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Mathematics, 2020 The history of boundary value problems for differential equations starts with the well-known studies of D. Bernoulli, J. D’Alambert, C. Sturm, J. Liouville, L. Euler, G. Birkhoff and V. Steklov.
Oktay Sh. Mukhtarov, Merve Yücel
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Evolutionary Problems Involving Sturm–Liouville Operators [PDF]
, 2013 The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in earlier works for a special case and later extended to more general evolutionary problems. We are here concerned with the $(1+1)$ -dimensional evolutionary case, which in a particular case results in a hyperbolic partial differential equation ...
Picard, Rainer, Watson, Bruce
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Ramanujan’s master theorem for sturm liouville operator
Monatshefte für Mathematik, 2022 In this paper we prove an analogue of Ramanujan's master theorem in the setting of Sturm Liouville operator.
K. Jotsaroop, Sanjoy Pusti
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