Results 241 to 250 of about 138,809 (284)

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.
openaire   +1 more source

Eigenfunctions of Ordinary Differential Euler Operators

Journal of Mathematical Sciences, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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. The set of almost-commuting operators enjoys a richer structure that allows the computation of these centralizers. We present a method to calculate a basis
Jiménez-Pastor, Antonio; id_orcid 0000-0002-6096-0623, Rueda, Sonia L., Zurro, Maria Angeles   +2 more
openaire   +2 more sources

Hypoelliptic ordinary differential operators

Israel Journal of Mathematics, 1972
Necessary and sufficient conditions for the hypoellipticity of an ordinary differential operator withC ∞ coefficients in a neighborhood of a zero of finite order of the leading term are given. A sufficient condition for such an operator to be in a certain Hormander class is also given.
openaire   +2 more sources

Ordinary Differential Operators

1978
The basic theory of second-order ordinary differential operators, largely due to Hermann Weyl, is summarized in this chapter.
openaire   +1 more source

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 ...
openaire   +1 more source

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.
openaire   +2 more sources

Transformations of Ordinary Differential Operators

1981
Kummer-Liouville coordinate changes are presented for fourth order vector differential operators of the formally self-adjoint form. This study is preliminary to the development of canonical forms and transformation theory for linear fourth order partial differential operators.
Calvin D. Ahlbrandt, Don B. Hinton, Roger T. Lewis   +2 more
openaire   +1 more source

Onn-Fold Expansions for Ordinary Differential Operators

Mathematische Nachrichten, 2002
The authors apply results for abstract operator pencils (concerning \(n\)-fold expansions with respect to the eigen- and associated vectors of the pencil) to the differential equation \[ i^mu^{(m)} + p_1(x,\lambda)u^{(m-1)} +\dots + p_{m-1}(x,\lambda)u' + [p_m(x,\lambda) - \lambda^n]u = 0.
Faierman, M., Markus, A., Matsaev, V., Möller, M.   +3 more
openaire   +2 more sources

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 Green's function (4, 5, 7), or one can use the spectral theorem for unbounded operators (2, 3, 9 ...
openaire   +2 more sources