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Reconstruction of Higher-Order Differential Operators by Their Spectral Data
Mathematics, 2022 This paper is concerned with inverse spectral problems for higher-order (n>2) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either regular or ...
Natalia P. Bondarenko
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Computing Almost-Commuting Basis of Ordinary Differential Operators
ACM Communications in Computer Algebra, 2023 An effective computation of a basis of a nontrivial centralizer of a differential operator is the first step towards a Picard-Vessiot theory for spectral problems of ordinary differential operators.
Antonio Jimenez-Pastor +2 more
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Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators
Mathematics, 2021 The main objective of our paper is to focus on the study of sequences (finite or countable) of groups and hypergroups of linear differential operators of decreasing orders.
Jan Chvalina +3 more
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Characterization of domains of self-adjoint ordinary differential operators of any order, even or odd [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2017 We characterize the domains of very general ordinary differential operators of any order, even or odd, with complex coefficients and arbitrary deficiency index.
Xiaoling Hao +3 more
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Spectral analysis of singular ordinary differential operators with indefinite weights
Journal of Differential Equations, 2010 In this paper we develop a perturbation approach to investigate spectral problems for singular ordinary differential operators with indefinite weight functions.
Jussi Behrndt, Friedrich Philipp
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Perturbation of ordinary differential operators
Journal of Mathematical Analysis and Applications, 1966 A perturbation theorem is proved which enables us to extend the results of J. Schwartz and others, to the effect that a wide class of boundary value problems for ordinary differential operators with operator valued coefficients generate unbounded ...
Turner, Robert E.L
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A note on generalized resolvents for ordinary differential operators [PDF]
Proceedings of the American Mathematical Society, 1976 We give an explicit construction for the kernel of an arbitrary generalized resolvent for an ordinary symmetric differential operator. In particular, this avoids the use of approximation of selfadjoint operators on compact intervals.
Sung J. Lee
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Normal forms for ordinary differential operators, I
Proceedings of the Steklov Institute of MathematicsIn this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain two applications in different directions of algebra/algebraic geometry.
Guo, J., Zheglov, A. B.
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Green's Functions for Singular Ordinary Differential Operators
Canadian Journal of Mathematics, 1967 There are several ways to approach the eigenfunction expansion problem for ordinary differential operators via the spectral theorem for self-ad joint linear operators in Hilbert space. One can examine the resolvent, which requires a detailed study of the
Fred Brauer
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On weighted positivity of ordinary differential operators
Journal of Inequalities and Applications, 1999 Some elliptic differential operators possess a weighted positivity property, where the weight is a fundamental solution of the operator. This property has interesting applications to partial differential operators.
Eilertsen Stefan
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