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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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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Normal Forms for Ordinary Differential Operators. III
Proceedings of the Steklov Institute of Mathematics40 p; V2: minor changes, to appear in Proc. Steklov Inst. Math. This is part 3 of a split version.
Guo, J., Zheglov, A. B.
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Perturbation of ordinary differential operators
Journal of Mathematical Analysis and Applications, 1966 AbstractA 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 spectral operators in the L2 space over a finite interval.
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. We also discuss integrability of functions which are adjoint to certain fundamental solutions.
Sung J. Lee
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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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Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order
Mathematics, 2020 We investigate the initial problem for a linear system of ordinary differential equations with constant coefficients and with the Dzhrbashyan–Nersesyan fractional differentiation operator.
Murat Mamchuev
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Characterization of domains of symmetric and self-adjoint ordinary differential operators
Electronic Journal of Differential Equations, 2018 We characterize the two point boundary conditions which determine symmetric ordinary differential operators of any order, even or odd, with complex coefficients and arbitrary deficiency index, in a Hilbert space.The self-adjoint characterizations ...
Aiping Wang, Anton Zettl
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Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Groebner Bases [PDF]
, 2010 We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential algebras.
Regensburger, Georg +4 more
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On linear systems and τ functions associated with Lamé's equation and Painlevé's equation VI. [PDF]
, 2011 Painleve's transcendental differential equation PVI may be expressed as the consistency condition for a pair of linear differential equations with 2 by 2 matrix coefficients with rational entries.
Gordon Blower, Blower, Gordon
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