Reflectionless Herglotz Functions and Jacobi Matrices
β Scribed by Alexei Poltoratski; Christian Remling
- Publisher
- Springer
- Year
- 2008
- Tongue
- English
- Weight
- 239 KB
- Volume
- 288
- Category
- Article
- ISSN
- 0010-3616
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π SIMILAR VOLUMES
## Abstract By a general argument, it is shown that Herglotz wave functions are dense (with respect to the C^β^(Ξ©)βtopology) in the space of all solutions to the reduced wave equation in Ξ©. This is used to provide corresponding approximation results in global spaces (eg. in L2βSobolevβspaces __H__^
We provide a comprehensive analysis of matrix -valued Herglotz functions and illustrate their applications in the spectral theory of self -adjoint Hamiltonian systems including matrixvalued SchrΓΆdinger and Dirac -type operators. Special emphasis is devoted to appropriate matrixvalued extensions of t
## Abstract Let __D__ββ^3^ be a bounded domain with connected boundary __Ξ΄D__ of class __C__^2^. It is shown that Herglotz wave functions are dense in the space of solutions to the Helmholtz equation with respect to the norm in __H__^1^(__D__) and that the electric fields of electromagnetic Herglot