| 1. |
- Nordebo, Sven, et al.
(author)
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Fisher information for inverse problems and trace class operators
- 2012
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In: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 53:12
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Journal article (peer-reviewed)abstract
- This paper provides a mathematical framework for Fisher information analysis forinverse problems based on Gaussian noise on infinite-dimensional Hilbert space. The covariance operator for the Gaussian noise is assumed to be trace class, andthe Jacobian of the forward operator Hilbert-Schmidt. We show that the appropriatespace for defining the Fisher information is given by the Cameron-Martin space. This is mainly because the range space of the covariance operator always is strictlysmaller than the Hilbert space. For the Fisher information to be well-defined, it is furthermore required that the range space of the Jacobian is contained in the Cameron-Martin space. In order for this condition to hold and for the Fisher information tobe trace class, a sufficient condition is formulated based on the singular values ofthe Jacobian as well as of the eigenvalues of the covariance operator, together withsome regularity assumptions regarding their relative rate of convergence. An explicit example is given regarding an electromagnetic inverse source problem with “external”spherically isotropic noise, as well as “internal” additive uncorrelated noise.
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| 2. |
- Nordebo, Sven, et al.
(author)
-
On the generalized Jordan's lemma with applications in waveguide theory
- 2013
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In: Proceeding of 2013 URSI International Symposium on Electromagnetic Theory (EMTS). - 9784885522772 ; , s. 1039-1042
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Conference paper (peer-reviewed)abstract
- This paper presents two variants of a generalized Jordan's lemma with applications in waveguide theory. As a main application is considered an asymptotic analysis for open waveguide structures with circular geometry. In particular, the generalized Jordan's lemma can be used to justify that field components can be calculated as the sum of discrete and non-discrete modes, i.e., as the sum of residues and an integral along the branch-cut defined by the transversal wavenumber of the exterior domain. An explicit example regarding the axial symmetric TM0 modes of a single core transmission line, wire, or optical fibre is included to demonstrate the associated asymptotic behavior for a typical open waveguide structure.
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| 3. |
- Toft, Joachim, 1964-, et al.
(author)
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Decompositions of Gelfand-Shilov kernels into kernels of similar class
- 2012
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In: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 396:1, s. 315-322
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Journal article (peer-reviewed)abstract
- We prove that any linear operator with kernel in a Gelfand-Shilov space is a composition of two operators with kernels in the same Gelfand-Shilov space. We also give links on numerical approximations for such compositions. We apply these composition rules to establish Schatten-von Neumann properties for such operators.
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