{"title":"The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach","authors":"M. Brown, M. Marletta, S. Naboko, I. Wood","doi":"10.1090/spmj/1792","DOIUrl":null,"url":null,"abstract":"<p>This paper is a contribution to the theory of functional models. In particular, it develops the so-called spectral form of the functional model where the selfadjoint dilation of the operator is represented as the operator of multiplication by an independent variable in some auxiliary vector-valued function space. With the help of a Lagrange identity, in the present version the relationship between this auxiliary space and the original Hilbert space will be explicit. A simple example is provided.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":"15 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1792","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is a contribution to the theory of functional models. In particular, it develops the so-called spectral form of the functional model where the selfadjoint dilation of the operator is represented as the operator of multiplication by an independent variable in some auxiliary vector-valued function space. With the help of a Lagrange identity, in the present version the relationship between this auxiliary space and the original Hilbert space will be explicit. A simple example is provided.
期刊介绍:
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.