The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations Article Swipe
Jean Fornerod
,
Hoài-Minh Nguyên
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2107.05507
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2107.05507
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreteness of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish the completeness of the generalized eigenfunctions and derive an optimal upper bound for the counting function under these conditions, assuming additionally that the coefficients are twice continuously differentiable. The approach is based on the spectral theory of Hilbert-Schmidt operators.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2107.05507
- https://arxiv.org/pdf/2107.05507
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4287080196
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https://openalex.org/W4287080196Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2107.05507Digital Object Identifier
- Title
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The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equationsWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
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2021-07-12Full publication date if available
- Authors
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Jean Fornerod, Hoài-Minh NguyênList of authors in order
- Landing page
-
https://arxiv.org/abs/2107.05507Publisher landing page
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https://arxiv.org/pdf/2107.05507Direct link to full text PDF
- Open access
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2107.05507Direct OA link when available
- Concepts
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Eigenfunction, Completeness (order theory), Mathematics, Eigenvalues and eigenvectors, Upper and lower bounds, Differentiable function, Mathematical analysis, Maxwell's equations, Function (biology), Hilbert space, Applied mathematics, Physics, Quantum mechanics, Biology, Evolutionary biologyTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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