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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, Sonia L Rueda, Maria-Angeles Zurro   +2 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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Ordinary Differential Equations and Operators

Lecture Notes in Mathematics, 1983
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Regular Ordinary Differential Operators with Involution

Mathematical Notes, 2019
The paper under review deals with the operators defined on a finite closed interval by differential expressions of the form \[L(y)=JP(y)+Q(y), \quad y=y(x), \quad x\in[-1,1],\] where \[P(y)=y^{(n)}(x)+\sum_{k=1}^{n} p_k (x)y^{(n-k)},\;\; Q(y)=y^{(m)}(x)+\sum_{k=1}^{m} q_k (x)y^{(m-k)};\] \(J\) is the involution operator \(Jy(x)=y(-x)\) and the ...
Vladykina, V. E., Shkalikov, A. A.
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Eigenfunctions of Ordinary Differential Euler Operators

Journal of Mathematical Sciences, 2020
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Spectral Properties of Ordinary Differential Operators with Involution

Doklady Mathematics, 2019
Let P and Q be ordinary differential operators of order n and m generated by s = max{n; m} boundary conditions on a nite interval [a; b]. We study operators of the form L = JP + Q, where J is the involution operator in the space L2[a; b]. We consider three cases n > m, n < m, and n = m, for which we dene concepts of regular, almost regular, and ...
Vladykina, V. E., Shkalikov, A. A.
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On the Essential Spectra of Ordinary Differential Operators

American Journal of Mathematics, 1954
(1) y" + + q)y 0, let A be a real parameter and q = q (t) a real-valued contilluous function on 0 ? t < oo. When (1) is of the limit-point type (in the sense of Weyl [10]), let S' denote its essential spectrum, that is, the set of cluster points A of the spectrum of the self-adjoint operator associated with (1) and a homnogeneouboundary condition at t =
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Factorization of differential operators with ordinary differential polynomial coefficients

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, 2012
In this paper, we present an algorithm to factor a differential operator L = σn + cn 1σn-1 + ··· + c1σ+c0 with coefficients ci in C{y}, where C is a constant field and C{y} is the ordinary differential polynomial ring over C. Also, we discuss the applications of the algorithm in decomposing nonlinear differential polynomials and factoring differential ...
Mingbo Zhang, Yong Luo
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Ordinary Differential Operators

1987
It is natural to begin the study of those aspects of the theory of boundary value problems that are of interest here with a rather detailed discussion of a number of properties of ordinary differential equations. In the first place, ordinary differential Operations are the simplest entities in the theory in which we are interested that can, in many ...
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Ordinary Differential Operators

1978
The basic theory of second-order ordinary differential operators, largely due to Hermann Weyl, is summarized in this chapter.
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