| 1. |
- Aleksandrov, Alexei, et al.
(författare)
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Finite rank Toeplitz operators: some extensions of D. Luecking's theorem.
- 2009
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 256:7, s. 2291-2303
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Tidskriftsartikel (refereegranskat)abstract
- The recent theorem by D. Luecking about finite rank Bergman-Toeplitz operators is extended to weights being distributions with compact support and to the spaces of harmonic functions. © 2008 Elsevier Inc. All rights reserved.
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| 2. |
- Borichev, A.A., et al.
(författare)
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The Finite Rank Theorem for Toeplitz Operators on the Fock Space
- 2015
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Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 25:1, s. 347-356
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Tidskriftsartikel (refereegranskat)abstract
- We consider Toeplitz operators on the Fock space, under rather general conditions imposed on the symbols. We prove that if a Toeplitz operator has finite rank, then the operator and its symbol are zero. Our argument is somewhat different from the ones used previously for finite rank theorem, and it enables us to get rid of the compact support condition and even allows for a certain growth of the symbol.
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| 3. |
- Esmeral, K., et al.
(författare)
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L–Invariant Fock–Carleson Type Measures for Derivatives of Order k and the Corresponding Toeplitz Operators
- 2019
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Ingår i: Journal of Mathematical Sciences. - : Springer Science and Business Media LLC. - 1072-3374 .- 1573-8795. ; 242:2, s. 337-358
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Tidskriftsartikel (refereegranskat)abstract
- Our purpose is to characterize the so-called horizontal Fock–Carleson type measures for derivatives of order k (we write it k-hFC for short) for the Fock space as well as the Toeplitz operators generated by sesquilinear forms given by them. We introduce real coderivatives of k-hFC type measures and show that the C*-algebra generated by Toeplitz operators with the corresponding class of symbols is commutative and isometrically isomorphic to a certain C*-subalgebra of L∞(ℝn). The above results are extended to measures that are invariant under translations along Lagrangian planes. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
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| 4. |
- Marlettta, Marco, et al.
(författare)
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A Laplace operator with boundary conditions singular at one point
- 2009
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Ingår i: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 42:12
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Tidskriftsartikel (refereegranskat)abstract
- We discuss a recent paper of Berry and Dennis (J. Phys. A: Math. Theor. 2008 41 135203) concerning a Laplace operator on a smooth domain with singular boundary condition. We explain a paradox in the article (J. Phys. A: Math. Theor. 2008 41 135203) and show that if a certain additional condition is imposed, the result is a spectral problem for a self-adjoint operator having only eigenvalues and no continuous spectrum. The eigenvalues accumulate at ±∞ only, and we obtain the asymptotic behaviours of the counting functions n+(λ) and n−(λ) for positive and negative eigenvalues. The physical meaning of the additional boundary condition is not yet clear.
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| 6. |
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| 7. |
- Miyanishi, Y., et al.
(författare)
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Spectral properties of the Neumann-Poincaré operator in 3D elasticity
- 2021
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Ingår i: International Mathematics Research Notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; 1921:11, s. 8715-8740
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Tidskriftsartikel (refereegranskat)abstract
- For the Neumann-Poincare operator in 3D elasticity, the location of the essential spectrum is found, both for a homogeneous and non-homogeneous material and the rate of convergence of eigenvalues to the tips of the essential spectrum is estimated.
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| 8. |
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| 9. |
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| 10. |
- Nursultanov, Medet, et al.
(författare)
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Eigenvalue asymptotics for the sturm-liouville operator with potential having a strong local negative singularity
- 2017
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Ingår i: Opuscula Mathematica. - 1232-9274 .- 2300-6919. ; 37, s. 109-139
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Tidskriftsartikel (refereegranskat)abstract
- © Wydawnictwa AGH, Krakow 2017.We find asymptotic formulas for the eigenvalues of the Sturm-Liouville operator on the finite interval, with potential having a strong negative singularity at one endpoint. This is the case of limit circle in H. Weyl sense. We establish that, unlike the case of an infinite interval, the asymptotics for positive eigenvalues does not depend on the potential and it is the same as in the regular case. The asymptotics of the negative eigenvalues may depend on the potential quite strongly, however there are always asymptotically fewer negative eigenvalues than positive ones. By unknown reasons this type of problems had not been studied previously.
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