Skip to main content

The functional model for maximal dissipative operators (translation form): An approach in the spirit of operator knots

Brown, Malcolm, Marletta, Marco, Naboko, Serguei, Wood, Ian (2020) The functional model for maximal dissipative operators (translation form): An approach in the spirit of operator knots. Transactions of the American Mathematical Society, 373 . pp. 4145-4187. ISSN 0002-9947. E-ISSN 1088-6850. (doi:10.1090/tran/8029) (KAR id:78967)

PDF Author's Accepted Manuscript
Language: English


Download (554kB) Preview
[thumbnail of FM_final.pdf]
Preview
This file may not be suitable for users of assistive technology.
Request an accessible format
Official URL
https://doi.org/10.1090/tran/8029

Abstract

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 ˇStraus 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 Schrödinger operator on a half-line with dissipative potential, and boundary condition and connections to existing theory are discussed.

Item Type: Article
DOI/Identification number: 10.1090/tran/8029
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 25 Nov 2019 12:31 UTC
Last Modified: 03 Mar 2021 16:38 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/78967 (The current URI for this page, for reference purposes)
Wood, Ian: https://orcid.org/0000-0001-7181-7075
  • Depositors only (login required):

Downloads

Downloads per month over past year