| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- Rohleder, Jonathan, 1984-
(författare)
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Inequalities between Neumann and Dirichlet eigenvalues of Schrödinger operators
- 2021
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Ingår i: Journal of Spectral Theory. - 1664-039X .- 1664-0403. ; 11:3, s. 915-933
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Tidskriftsartikel (refereegranskat)abstract
- Given a Schrödinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The obtained inequalities depend partially on monotonicity and convexity properties of the potential. The results are counterparts of classical inequalities for the Laplacian but display some distinction between the one-dimensional case and higher dimensions.
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| 5. |
- Rozenblioum, Grigori, 1948
(författare)
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Eigenvalues of singular measures and Connes' noncommutative integration.
- 2022
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Ingår i: Journal of Spectral Theory. - 1664-039X .- 1664-0403. ; 12:1, s. 259-300
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Tidskriftsartikel (refereegranskat)abstract
- In a domain Ω⊂R^N we consider compact, Birman–Schwinger type operators of the form T=A^∗P A with P being a Borel measure in Ω, containing a singular part, andA being an order −N/2 pseudodifferential operator. Operators are defined by means of quadratic forms. For a class of such operators, we obtain a proper version of H. Weyl's law for eigenvalues, with order not depending on dimensional characteristics of the measure. These results lead to establishing measurability, in the sense of Dixmier–Connes, of such operators and the noncommutative version of integration over Lipschitz surfaces and rectifiable sets.
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| 6. |
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| 7. |
- Torshage, Axel, 1991-
(författare)
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Enclosure of the Numerical Range and Resolvent Estimates of Non-Selfadjoint Operator Functions
- 2020
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Ingår i: Journal of Spectral Theory. - : European Mathematical Society Publishing House. - 1664-039X .- 1664-0403. ; 10:2, s. 379-413
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss the relationship between the numerical range of an extensive class of unbounded operator functions and the joint numerical range of the operator coefficients. Furthermore, we derive methods on how to find estimates of the joint numerical range. Those estimates are used to obtain explicitly computable enclosures of the numerical range of the operator function and resolvent estimates. The enclosure and upper estimate of the norm of the resolvent are optimal given the estimate of the joint numerical range.
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