Results 11 to 20 of about 860 (42)

B\"acklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem [PDF]

, 2007
A GBDT version of the Backlund-Darboux transformation is constructed for a non-isospectral canonical system, which plays essential role in the theory of random matrix models. The corresponding Riemann-Hilbert problem is treated and some explicit formulas
Sakhnovich, Alexander
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Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

, 2012
Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles.
Al-Gwaiz M. A., Atkinson F. V., Coddington E. A., Condon E. U., Julia Stasińska, Levitan B. M., Szmytkowski R., Titchmarsh E. C.   +7 more
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An inverse spectral problem for the matrix Sturm-Liouville operator on the half-line

, 2014
The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix.
Bondarenko, Natalia
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Essential spectra of difference operators on $\sZ^n$-periodic graphs

, 2007
Let $(\cX, \rho)$ be a discrete metric space. We suppose that the group $\sZ^n$ acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a $\sZ^n$-periodic discrete metric space.
Albeverio S Lakaev S N Muminov Z I, Berkolaiko G, Cycon H L, Deift P, Georgescu V Iftimovici A, Harris P, Jirari A, Kato T, Korotyaev E Lobanov I, Korotyaev E Lobanov I, Kuchment P, Kuchment P, Kuchment P (ed), Kuchment P Post O, Last Y Simon B, Lax P D, Mogilner A, Rabinovich V S, Rabinovich V S, Rabinovich V S, Reed M, Reed M, Roch S, Saito R, Steffen Roch, Vladimir S Rabinovich, Yafaev D R   +26 more
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Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube

, 2005
We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete ...
B. Chenaud, D. Borisov, D. Gilbarg, H. Kovařík, I.J. Clark, I.J. Clark, J. Goldstone, J.T. Londergan, M. Reed, P. Duclos, P. Exner, P. Exner, P. Exner, T. Ekholm, T. Kato, W. Renger   +15 more
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Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

, 2005
New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl ...
Ablowitz M J, Ablowitz M J, Alexander Sakhnovich, Boutet de Monvel A, Cascaval R C, Clark S Gesztesy F, Daletskij Yu L, Djakov P, Faddeev L D, Freiling G, Gesztesy F Zinchenko M, Grebert B, Levitan B M, Potapov V P, Sakhnovich A L, Sakhnovich A L, Sakhnovich A L, Sakhnovich A L, Sakhnovich L A, Sakhnovich L A, Sakhnovich L A, Sakhnovich L A, Simon B, Sulem C, Teschl G, Weikard R   +25 more
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Spectral Approximation for Quasiperiodic Jacobi Operators [PDF]

, 2014
Quasiperiodic Jacobi operators arise as mathematical models of quasicrystals and in more general studies of structures exhibiting aperiodic order. The spectra of these self-adjoint operators can be quite exotic, such as Cantor sets, and their fine ...
Embree, Mark, Fillman, Jake, Puelz, Charles   +2 more
core  

Nodal count of graph eigenfunctions via magnetic perturbation

, 2011
We establish a connection between the stability of an eigenvalue under a magnetic perturbation and the number of zeros of the corresponding eigenfunction. Namely, we consider an eigenfunction of discrete Laplacian on a graph and count the number of edges
Band, Bartholdi, Colin de Verdière, Colin de Verdière, Courant, Fiedler, Hofstadter, Kato, Shubin, Sturm, Sunada   +10 more
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Symmetry of bound and antibound states in the semiclassical limit

, 2007
We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h.
A.A. Abramov, B. Simon, David Bindel, E. Korotyaev, J.P. Boyd, L.D. Landau, M. Hitrik, M. Zworski, Maciej Zworski, P. Briet, R. Froese, S. Fujiye, T. Ramond, T. Regge   +13 more
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Weyl asymptotics of the transmission eigenvalues for a constant index of refraction

, 2013
We prove Weyl type of asymptotic formulas for the real and the complex internal transmission eigenvalues when the domain is a ball and the index of refraction is ...
Pham, Ha, Stefanov, Plamen
core   +3 more sources