Functional model for boundary-value problems
arXiv:1907.08144 · doi:10.1112/mtk.12092
Abstract
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of the associated generalised Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems as well as in the study of their spectra.
25 pages, 1 figure
References in corpus (6)
- Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I
- Spectral asymptotics for Robin problems with a discontinuous coefficient
- Time-Dispersive Behaviour as a Feature of Critical Contrast Media
- Functional model for extensions of symmetric operators and applications to scattering theory
- The functional model for maximal dissipative operators: An approach in the spirit of operator knots
- Scattering theory for a class of non-selfadjoint extensions of symmetric operators