| 1. |
- Helsing, Johan, et al.
(författare)
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Dirac Integral Equations for Dielectric and Plasmonic Scattering
- 2021
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 93:5
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Tidskriftsartikel (refereegranskat)abstract
- A new integral equation formulation is presented for the Maxwell transmission problem in Lipschitz domains. It builds on the Cauchy integral for the Dirac equation, is free from false eigenwavenumbers for a wider range of permittivities than other known formulations, can be used for magnetic materials, is applicable in both two and three dimensions, and does not suffer from any low-frequency breakdown. Numerical results for the two-dimensional version of the formulation, including examples featuring surface plasmon waves, demonstrate competitiveness relative to state-of-the-art integral formulations that are constrained to two dimensions. However, our Dirac integral equation performs equally well in three dimensions, as demonstrated in a companion paper.
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| 2. |
- Partington, Jonathan R., et al.
(författare)
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Laplace–Carleson Embeddings on Model Spaces and Boundedness of Truncated Hankel and Toeplitz Operators
- 2020
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 92:4
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Tidskriftsartikel (refereegranskat)abstract
- A characterisation is given of bounded embeddings from weighted L2 spaces on bounded intervals into L2 spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen spaces). As an application necessary and sufficient conditions are given for the boundedness of truncated Hankel and Toeplitz integral operators, including the weighted case, and on model spaces.
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| 3. |
- Rozenblioum, Grigori, 1948, et al.
(författare)
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Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach
- 2022
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 94:3
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Tidskriftsartikel (refereegranskat)abstract
- For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint operators. We discuss main properties of these representation and, especially, describe relations between properties of the spectral function of Toeplitz operators in the spectral representation and properties of the symbols.
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