最大耗散算子的函数模型谱形式：拉格朗日特性方法

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2024-04-12 DOI:10.1090/spmj/1792

M. Brown, M. Marletta, S. Naboko, I. Wood

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引用次数: 0

摘要

本文是对函数模型理论的贡献。特别是，它发展了函数模型的所谓谱形式，其中运算符的自交扩张被表示为在某个辅助向量值函数空间中与自变量相乘的运算符。借助拉格朗日特性，在本版本中，该辅助空间与原始希尔伯特空间之间的关系将被明确化。下面提供一个简单的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach

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.

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

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.