| 1. |
- Abatangelo, Laura, et al.
(författare)
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Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators
- 2019
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Ingår i: Journal of Spectral Theory. - 1664-039X .- 1664-0403. ; 9:2, s. 379-427
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Tidskriftsartikel (refereegranskat)abstract
- We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov–Bohm operators with two colliding poles moving on an axis of symmetry of the domain.
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| 2. |
- Ameur, Yacin, et al.
(författare)
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Exponential moments for disk counting statistics at the hard edge of random normal matrices
- 2023
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Ingår i: Journal of Spectral Theory. - : European Mathematical Society - EMS - Publishing House GmbH. - 1664-039X .- 1664-0403. ; 13:3, s. 841-902
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Tidskriftsartikel (refereegranskat)abstract
- We consider the multivariate moment generating function of the disk counting statistics of a model Mittag-Leffler ensemble in the presence of a hard wall. Let n be the number of points. We focus on two regimes: (a) the “hard edge regime” where all disk boundaries are at a distance of order n1 from the hard wall, and (b) the “semi-hard edge regime” where all disk boundaries are at a distance of order √1n from the hard wall. As n → + ∞, we prove that the moment generating function enjoys asymptotics of the form (Equation presented) In both cases, we determine the constants C1;:::; C4 explicitly. We also derive precise asymptotic formulas for all joint cumulants of the disk counting function, and establish several central limit theorems. Surprisingly, and in contrast to the “bulk”, “soft edge”, and “semi-hard edge” regimes, the second and higher order cumulants of the disk counting function in the “hard edge” regime are proportional to n and not to √n.
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| 3. |
- Behrndt, Jussi, et al.
(författare)
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Eigenvalue inequalities for Schrödinger operators on unbounded Lipschitz domains
- 2018
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Ingår i: Journal of Spectral Theory. - 1664-039X .- 1664-0403. ; 8:2, s. 493-508
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Tidskriftsartikel (refereegranskat)abstract
- Given a Schrödinger differential expression on an exterior Lipschitz domain we prove strict inequalities between the eigenvalues of the corresponding selfadjoint operators subject toDirichlet andNeumann orDirichlet andmixed boundary conditions, respectively. Moreover, we prove a strict inequality between the eigenvalues of two different elliptic differential operators on the same domain with Dirichlet boundary conditions.
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| 4. |
- Bjerklöv, Kristian, Docent, et al.
(författare)
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Coexistence of absolutely continuous and pure point spectrum for kicked quasiperiodic potentials
- 2021
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Ingår i: Journal of Spectral Theory. - : European Mathematical Society - EMS - Publishing House GmbH. - 1664-039X .- 1664-0403. ; 11:3, s. 1215-1254
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a class of real analytic "peaky" potentials for which the corresponding quasiperiodic 1D-Schrodinger operators exhibit, for quasiperiodic frequencies in a set of positive Lebesgue measure, both absolutely continuous and pure point spectrum.
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| 5. |
- De Teran, Fernando, et al.
(författare)
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Generic symmetric matrix pencils with bounded rank
- 2020
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Ingår i: Journal of Spectral Theory. - : EMS Publishing House. - 1664-039X .- 1664-0403. ; 10:3, s. 905-926
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Tidskriftsartikel (refereegranskat)abstract
- We show that the set of n x n complex symmetric matrix pencils of rank at most r is the union of the closures of left perpendicular r/2 Right perpendicular + 1 sets of matrix pencils with some, explicitly described, complete eigenstructures. As a consequence, these are the generic complete eigenstructures of n x n complex symmetric matrix pencils of rank at most r. We also show that the irreducible components of the set of n x n symmetric matrix pencils with rank at most r, when considered as an algebraic set, are among these closures.
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| 6. |
- Frank, Rupert L., et al.
(författare)
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The BCS critical temperature in a weak homogeneous magnetic field
- 2019
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Ingår i: Journal of Spectral Theory. - : European Mathematical Society - EMS - Publishing House GmbH. - 1664-039X .- 1664-0403. ; 9:3, s. 1005-1062
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Tidskriftsartikel (refereegranskat)abstract
- We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature fromWHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.
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| 7. |
- Goffeng, Magnus C H T, 1987, et al.
(författare)
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Spectral flow of exterior Landau-Robin hamiltonians
- 2017
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Ingår i: Journal of Spectral Theory. - 1664-039X .- 1664-0403. ; 70, s. 847-879
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Tidskriftsartikel (refereegranskat)abstract
- © European Mathematical Society. We study the spectral flow of Landau-Robin hamiltonians in the exterior of a compact domain with smooth boundary. This provides a method to study the spectrum of the exterior Landau-Robin hamiltonian's dependence on the choice of Robin data, even explaining the heuristics of how the spectrum of the Robin problem asymptotically tends to the spectrum of the Dirichlet problem. The main technical result concerns the continuous dependence of Landau-Robin hamiltonians on the Robin data in the gap topology. The problem can be localized to the compact boundary where the asymptotic behavior of the spectral flow in some special cases can be described.
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| 8. |
- Kozlov, Vladimir, et al.
(författare)
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Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators
- 2016
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Ingår i: Journal of Spectral Theory. - : EUROPEAN MATHEMATICAL SOC. - 1664-039X .- 1664-0403. ; 6:1, s. 99-135
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain. The proximity of two domains is measured in terms of the norm of the difference between the two resolvents corresponding to the reference domain and the perturbed domain, and the size of eigenfunctions outside the intersection of the two domains. This construction enables the possibility of comparing both nonsmooth domains and domains with different topology. An abstract framework is presented, where the main result is an asymptotic formula where the remainder is expressed in terms of the proximity quantity described above when this is relatively small. As an application, we develop a theory for the Laplacian in Lipschitz domains. In particular, if the domains are assumed to be C-1,C-alpha regular, an asymptotic result for the eigenvalues is given together with estimates for the remainder, and we also provide an example which demonstrates the sharpness of our obtained result.
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| 9. |
- Kurasov, Pavel, et al.
(författare)
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Rayleigh estimates for differential operators on graphs
- 2014
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Ingår i: Journal of Spectral Theory. - 1664-039X .- 1664-0403. ; 4:2, s. 211-219
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Tidskriftsartikel (refereegranskat)abstract
- We study the spectral gap, i.e. the distance between the two lowest eigenvalues for Laplace operators on metric graphs. A universal lower estimate for the spectral gap is proven and it is shown that it is attained if the graph is formed by just one interval. Uniqueness of the minimizer allows to prove a geometric version of the Ambartsumian theorem derived originally for Schrodinger operators.
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| 10. |
- Larson, Simon
(författare)
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Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains
- 2019
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Ingår i: Journal of Spectral Theory. - : EUROPEAN MATHEMATICAL SOC. - 1664-039X .- 1664-0403. ; 9:3, s. 857-895
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Tidskriftsartikel (refereegranskat)abstract
- For Omega subset of R-n, a convex and bounded domain, we study the spectrum of -Delta(Omega) the Dirichlet Laplacian on Omega. For Lambda >= 0 and gamma >= 0 let Omega(Lambda,gamma)(A) denote any extremal set of the shape optimization problem sup {Tr(-Delta(Omega) - Lambda)(gamma) : Omega is an element of .A, vertical bar Omega vertical bar = 1}, where A is an admissible family of convex domains in R-n. If gamma >= 1 and (1) and {Lambda(j)}(j >= 1) is a positive sequence tending to infinity we prove that {Omega Lambda j , gamma(A)}(j >= 1) is a bounded sequence, and hence contains a convergent subsequence. Under an additional assumption on A we characterize the possible limits of such subsequences asminimizers of the perimeter among domains in A of unit measure. For instance if A is the set of all convex polygons with no more than m faces, then Omega(Lambda,gamma) converges, up to rotation and translation, to the regular m-gon.
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