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

Brown, B. Malcolm, Marletta, Marco, Naboko, Serguei and 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. 10.1090/tran/8029

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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 Štraus 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
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Publisher: American Mathematical Society
ISSN: 0002-9947
Date of First Compliant Deposit: 14 November 2019
Date of Acceptance: 20 October 2019
Last Modified: 30 Jul 2020 15:12
URI: http://orca.cf.ac.uk/id/eprint/126797

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