Results 271 to 280 of about 328,940 (311)

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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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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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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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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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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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 ...
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Functional determinants for ordinary differential operators

Journal of Physics A: Mathematical and General, 1992
Summary: We study the analytic properties of regularized functional determinants for ordinary differential operators. To this end a new regularization scheme is introduced. Relations between different approaches are analysed and the connection between the presence of divergent traces and regularization differences is discussed.
Gamboa Saraví, R. E., Rossini, G. L., Fuentes, M.   +2 more
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Semibounded Extensions of Singular Ordinary Differential Operators

Canadian Mathematical Bulletin, 1988
AbstractThe self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.
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Hecke Operators on Linear Ordinary Differential Equations

Acta Applicandae Mathematica, 1999
The theory of automorphic forms and that of ordinary linear differential equations are closely related. Automorphic forms are common eigenforms of certain Hecke operators. Thus it is natural to consider the Hecke operators acting on the space of ordinary differential equations associated with automorphic forms.
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On -meromorphic ordinary differential operators

, 2016
P. Grinevich, S. Novikov
semanticscholar   +1 more source