Results 241 to 250 of about 2,195,788 (280)

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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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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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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The Two-Sided Factorization of Ordinary Differential Operators

Canadian Journal of Mathematics, 1980
Throughout this paper we shall use I to denote a given interval, not necessarily bounded, of real numbers and Cn to denote the real valued n times continuously differentiable functions on I and C0 will be abbreviated to C. By a differential operator of order n we shall mean a linear function L:Cn → C of the form1.1where pn(x) ≠ 0 for x ∊ I and pi ∊ Cj ...
Browne, Patrick J., Nillsen, Rodney
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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
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On isomorphism of ordinary differential operators

Applicable Analysis, 2004
The article deals with an ordinary linear differential operator L of even order 2m with constant coefficients which defines a natural mapping of the space to itself. The operator L is considered under an extra condition that its characteristic polynomial has no real roots and exactly m roots with strictly positive imaginary part. This work prepares the
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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.
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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
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