A Functional Model, Eigenvalues, and Finite Singular Critical Points for Indefinite Sturm-Liouville Operators
TLDR
In this paper, the essential spectrum of a weighted Sturm-Liouville operator is studied under the assumption that the weight function has one turning point, and an abstract approach to the problem is given via a functional model for indefinite Sturm Liouville operators.Abstract:
Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered.read more
Citations
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Journal ArticleDOI
Reviews - Eigenfunction Expansions Associated with Second-Order Differential Equations. By E. C. Titchmarsh Pp. 175. 20s. 1946. (Oxford University)
Journal ArticleDOI
The similarity problem for indefinite Sturm–Liouville operators and the HELP inequality
TL;DR: In this article, the authors studied the similarity problem for the indefinite Sturm-Liouville operator A = − ( sgn x ) d w d x d r d x acting in L w 2 ( − b, b ).
Book ChapterDOI
Some Remarks on the Spectral Problem Underlying the Camassa-Holm Hierarchy
Fritz Gesztesy,Rudi Weikard +1 more
TL;DR: In this paper, a generalization of the left-definite eigenvalue problem has been studied, where a Schrodinger or Sturm-Liouville operator T is associated with a differential expression of the form
Journal ArticleDOI
The Similarity Problem for Indefinite Sturm-Liouville Operators With Periodic Coefficients
TL;DR: In this article, the problem of similarity to a self-adjoint operator for J -positive Sturm-Liouville operators with 2π -periodic coefficients q and ω was investigated.
Journal ArticleDOI
Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential
Michael Levitin,Marcello Seri +1 more
TL;DR: For a particular family of long-range potentials, the authors showed that the eigenvalues of the indefinite Sturm-Liouville operator accumulate to zero asymptotically along specific curves in the complex plane.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Book
Theory of linear operators in Hilbert space
N. I. Akhiezer,I. M. Glazman +1 more
TL;DR: In this article, the main properties of bounded and unbounded operators, adjoint operators, symmetric and self-adjoint operators in hilbert spaces are discussed, as well as the stability of self-jointness under small perturbations.
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