- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Algebraic Nevanlinna operator functions and applications...
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Algebraic Nevanlinna operator functions and applications to electromagnetics Engstrom, Christian
Description
Operator functions with an algebraic dependence on a spectral parameter have applications in electromagnetic field theory, where the $\lambda$-dependent material properties are of Drude-Lorentz type. Let $M_\ell$, $\ell=1,2,\dots,L$ denote bounded linear operators in a Hilbert space $\mathcal H$ and denote by $A$ a self-adjoint operator with compact resolvent that is bounded from below. In this talk we consider operator functions of the form \[ \mathcal S(\lambda)=A-\lambda-\lambda\sum_{\ell=1}^L\dfrac{M_\ell}{c_\ell+id_{\ell}\sqrt{\lambda}-\lambda}, \quad \text{dom} \,\mathcal S(\lambda) = \text{dom} \,A, \quad \lambda \in \mathbb{C} \setminus P, \] where $P$ is the set of poles of the rational function and $c_\ell$, $d_{\ell}$ are non-negative constants. The operator function is self-adjoint if the damping $d_{\ell}$ is set to zero. Then we establish variational principles and provide optimal two-sided estimates for all the eigenvalues of $\mathcal S$. In the second part of the talk, I briefly present extensions to the non-self-adjoint case $d_{\ell}>0$ and ongoing work. The first part of the talk is based on a joint work with Heinz Langer and Christiane Tretter and the second part of the talk is based on a joint work with Axel Torshage.
Item Metadata
Title |
Algebraic Nevanlinna operator functions and applications to electromagnetics
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2019-10-07T17:26
|
Description |
Operator functions with an algebraic dependence on a spectral parameter have applications in electromagnetic field theory, where the $\lambda$-dependent material properties are of Drude-Lorentz type.
Let $M_\ell$, $\ell=1,2,\dots,L$ denote bounded linear operators in a Hilbert space $\mathcal H$ and denote by $A$ a self-adjoint operator with compact resolvent that is bounded from below. In this talk we consider operator functions of the form
\[
\mathcal S(\lambda)=A-\lambda-\lambda\sum_{\ell=1}^L\dfrac{M_\ell}{c_\ell+id_{\ell}\sqrt{\lambda}-\lambda},
\quad \text{dom} \,\mathcal S(\lambda) = \text{dom} \,A, \quad \lambda \in \mathbb{C} \setminus P,
\]
where $P$ is the set of poles of the rational function and $c_\ell$, $d_{\ell}$ are non-negative constants. The operator function is self-adjoint if the damping $d_{\ell}$ is set to zero. Then we establish variational principles and provide optimal two-sided estimates for all the eigenvalues of $\mathcal S$. In the second part of the talk, I briefly present extensions to the non-self-adjoint case $d_{\ell}>0$ and ongoing work.
The first part of the talk is based on a joint work with Heinz Langer and Christiane Tretter and the second part of the talk is based on a joint work with Axel Torshage.
|
Extent |
26.0 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Linneaus University
|
Series | |
Date Available |
2020-04-05
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0389740
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Researcher
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International