Recovering the M-channel Sturm-Liouville operator from M+1 spectra
نویسندگان
چکیده
منابع مشابه
Recovering the M - channel Sturm - Liouville operator from M + 1 spectra
For a system of M coupled Schrödinger equations, the relationship is found between the vector-valued norming constants and M + 1 spectra corresponding to the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The double set of norming vectors and associated spectrum of one of...
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y(0) cosα+ y′(0) sinα = 0, y(1) cosβ + y′(1) sinβ = 0 (2) y(0) cosα+ y′(0) sinα = 0, y(1) cos γ + y′(1) sin γ = 0 (3) with sin(γ − β) = 0, then q(x) is uniquely determined. Notice that this theorem does not include the case of Dirichlet (boundary conditions y(0) = y(1) = 0) and Neumann (boundary conditions of y′(0) = y′(1) = 0) spectra. Borg [1], Levinson [11], Isaacson, McKean and Trubowitz [8...
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In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...
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Abstract. We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori knowledge of the mean of the potential. Numerical examples show that the algorithm works quite reliable, even in the presence of noise. A proof of the ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2004
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1794844