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The Inverse Problem for Ordinary Differential Operators on the Line
American Journal of Mathematics, 1985In this interesting article the author investigates the linear differential operator (n\(\geq 2)\) \[ (1)\quad P=D^ n+q_{n-2}D^{n- 2}+...+q_ 0,\quad D=(1/i)d/dx \] \(q_ j\in L^ 1(R)\) for \(j=0,1,...,n-2\), being generally not self-adjoint. The inverse problem for the operator (1) on the line is the problem of determining the coefficients \(q_ 0,q_ 1,..
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Green's Functions for Singular Ordinary Differential Operators
Canadian Journal of Mathematics, 1967There 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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Minimum Moduli of Ordinary Differential Operators
Proceedings of the London Mathematical Society, 1971Goldberg, S., Meir, A.
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Semibounded Extensions of Singular Ordinary Differential Operators
Canadian Mathematical Bulletin, 1988AbstractThe 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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Computing Almost-Commuting Basis of Ordinary Differential Operators
ACM Communications in Computer Algebra, 2023María Ángeles Zurro +2 more
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On the Spectra of General Ordinary Quasi-Differential Operators and Their L2w-Solutions ()
Advances in Pure Mathematics, 2022Sobhy El-Sayed Ibrahim
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