| 1. |
- Kurasov, Pavel, et al.
(författare)
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Essential spectrum due to singularity
- 2003
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 10, s. 93-106
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Tidskriftsartikel (refereegranskat)abstract
- It is proven that the essential spectrum of any self-adjoint operator associated with the matrix differential expression [GRAPHICS] consists of two branches. One of these branches (called regularity spectrum) can be obtained by approximating the operator by regular operators (with coefficients which are bounded near the origin), the second branch (called singularity spectrum) appears due to singularity of the coefficients.
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| 2. |
- Kurasov, Pavel, et al.
(författare)
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On the essential spectrum of a class of singular matrix differential operators. I: Quasiregularity conditions and essential self-adjointness
- 2002
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Ingår i: Mathematical Physics, Analysis and Geometry. - 1385-0172. ; 5:3, s. 243-286
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Tidskriftsartikel (refereegranskat)abstract
- The essential spectrum of singular matrix differential operator determined by the operator matrix (-d/dx rho(x)d/dx + q(x) d/dx . beta/x - beta/x . d/dx m(x)/x(2))) is studied. It is proven that the essential spectrum of any self-adjoint operator associated with this expression consists of two branches. One of these branches (called regularity spectrum) can be obtained by approximating the operator by regular operators (with coefficients which are bounded near the origin), the second branch (called singularity spectrum) appears due to singularity of the coefficients.
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| 3. |
- Kurasov, Pavel, et al.
(författare)
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Spectral gap for quantum graphs and their edge connectivity
- 2013
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Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 46:27, s. 275309-
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Tidskriftsartikel (refereegranskat)abstract
- The spectral gap for Laplace operators on metric graphs and the relation between the graph's edge connectivity is investigated, in particular what happens to the gap if an edge is added to (or deleted from) a graph. It is shown that, in contrast to discrete graphs, the connection between the connectivity and the spectral gap is not one-to-one. The size of the spectral gap depends not only on the topology of the metric graph but on its geometric properties as well. It is shown that adding sufficiently large edges as well as cutting away sufficiently small edges leads to a decrease of the spectral gap. Corresponding explicit criteria are given.
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| 4. |
- Laptev, Ari, et al.
(författare)
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A Szego condition for a multidimensional Schrodinger operator
- 2005
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 219:2, s. 285-305
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Tidskriftsartikel (refereegranskat)abstract
- We consider spectral properties of a Schrodinger operator perturbed by a potential vanishing at infinity and prove that the corresponding spectral measure satisfies a Szego-type condition.
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| 5. |
- Laptev, Ari, et al.
(författare)
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Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials
- 2005
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 253:3, s. 611-631
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to extend a class of potentials for which the absolutely continuous spectrum of the corresponding multidimensional Schrodinger operator is essentially supported by [0, infinity). Our main theorem states that this property is preserved for slowly decaying potentials provided that there are some oscillations with respect to one of the variables.
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| 6. |
- Laptev, Ari, et al.
(författare)
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On new relations between spectral properties of Jacobi matrices and their coefficients
- 2003
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 241:1, s. 91-110
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Tidskriftsartikel (refereegranskat)abstract
- We study the spectral properties of Jacobi matrices. By using ``higher order'' trace formulae we obtain a result relating the properties of the elements of Jacobi matrices and the corresponding spectral measures. Complicated expressions for traces of some operators can be magically simplified allowing us to apply induction arguments. Our theorems are generalizations of a recent result of R. Killip and B. Simon [17].
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