| Autor: |
Brown, B. M., Marletta, M., Naboko, S., Wood, I. |
| Rok vydání: |
2018 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
In this article we develop a functional model for a general maximal dissipative operator. We construct the selfadjoint dilation of such operators. Unlike previous functional models, our model is given explicitly in terms of parameters of the original operator, making it more useful in concrete applications. For our construction we introduce an abstract framework for working with a maximal dissipative operator and its anti-dissipative adjoint and make use of the Straus characteristic function in our setting. Explicit formulae are given for the selfadjoint dilation, its resolvent, a core and the completely non-selfadjoint subspace; minimality of the dilation is shown. The abstract theory is illustrated by the example of a Schroedinger operator on a half-line with dissipative potential, and boundary condition and connections to existing theory are discussed. |
| Databáze: |
arXiv |
| Externí odkaz: |
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