Results 1 to 10 of about 328,940 (311)
Bispectral commutative ordinary differential operators.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1993 Let \(A\) be a commutative algebra of ordinary differential operators. We say \(A\) is bispectral if there is a family \(\psi(x,z)\) of joint eigenfunctions for the operators in \(A\) that also satisfies a differential equation of the form \(\Lambda\psi= \theta(x)\psi\), where \(\Lambda\) is some ordinary differential operator in the spectral parameter
G. Wilson
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Bispectral algebras of commuting ordinary differential operators [PDF]
Communications in Mathematical Physics, 1996 We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson.
Bakalov, B., Horozov, E., Yakimov, M.
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Commutative Ordinary Differential Operators [PDF]
Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1928 The paper is conveniently divided into two sections. The first contains the general argument and the main propositions unencumbered by proof: in the first paragraph of this section is collected material already published; the succeeding paragraphs of the
J. L. Burchnall, T. Chaundy
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Commuting Ordinary Differential Operators and the Dixmier Test [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 The Burchnall-Chaundy problem is classical in differential algebra, seeking to describe all commutative subalgebras of a ring of ordinary differential operators whose coefficients are functions in a given class.
E. Previato, Sonia L. Rueda, M. Zurro
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Fast Computation of Common Left Multiples of Linear Ordinary Differential Operators [PDF]
ACCA, 2012 We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs.
Bostan, Alin +3 more
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Invertible linear ordinary differential operators
Journal of Geometry and Physics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V. Chetverikov
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Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations [PDF]
Nonlinear Analysis, 2019 We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the
Moosa Moosa Gabeleh +2 more
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Commuting higher rank ordinary differential operators [PDF]
, 2012 In this paper we discuss some results related to commuting ordinary differential operators of rank greater than one.
A. Mironov
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Commutants of ordinary differential operators
Journal of Differential Equations, 1980 This paper is concerned with the algebraic and analytic structure of the commutant g’(L) of a regular ordinary differential operator L with Cz matrix-valued coefficients. The main algebraic result is that V(L) is a free module of rank at most EW over the polynomial ring U&L], where K is the six of the matrices in the coefficients of L and n is the ...
R. Carlson, K. Goodearl
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Extensions of dissipative operators with closable imaginary part [PDF]
Opuscula Mathematica, 2021 Given a dissipative operator \(A\) on a complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give a necessary and sufficient condition for an extension of \(A\) to still be ...
Christoph Fischbacher
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