<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative fourth order operators. </p></abstract>

In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative fourth order operators.

Functional Model of Dissipative Fourth Order Differential Operators

Department of Mathematics, Mehmet Akif Ersoy University of Burdur, 15100 Burdur, Turkey

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Functional Model of Dissipative Fourth Order Differential Operators"}

In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such...

Functional Model of Dissipative Fourth Order Differential Operators

Published Online: Sep 19, 2013

Page range: 237 - 252

DOI: https://doi.org/10.2478/auom-2013-0036

Keywords
Dilation, Dissipative operator, Completeness of the system of eigenvectors and associated vectors, Scattering matrix, Functional model, Characteristic function

This content is open access.

Functional Model of Dissipative Fourth Order Differential Operators

Published Online: Sep 19, 2013

Page range: 237 - 252

DOI: https://doi.org/10.2478/auom-2013-0036

KeywordsDilation, Dissipative operator, Completeness of the system of eigenvectors and associated vectors, Scattering matrix, Functional model, Characteristic function

This content is open access.

Keywords
Dilation, Dissipative operator, Completeness of the system of eigenvectors and associated vectors, Scattering matrix, Functional model, Characteristic function