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Titlebook: Completeness Theorems and Characteristic Matrix Functions; Applications to Inte Marinus A. Kaashoek,Sjoerd M. Verduyn Lunel Book 2022 The E

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发表于 2025-3-21 17:39:12 | 显示全部楼层 |阅读模式
书目名称Completeness Theorems and Characteristic Matrix Functions
副标题Applications to Inte
编辑Marinus A. Kaashoek,Sjoerd M. Verduyn Lunel
视频video
概述A new and self-contained study of linear operators that admit a characteristic matrix function.New completeness theorems for classes of Banach space operators motivated by applications.Comprehensive t
丛书名称Operator Theory: Advances and Applications
图书封面Titlebook: Completeness Theorems and Characteristic Matrix Functions; Applications to Inte Marinus A. Kaashoek,Sjoerd M. Verduyn Lunel Book 2022 The E
描述This monograph presents necessary and sufficient conditions for completeness of the linear span of eigenvectors and generalized eigenvectors of operators that admit a characteristic matrix function in a Banach space setting. Classical conditions for completeness based on the theory of entire functions are further developed for this specific class of operators. The classes of bounded operators that are investigated include trace class and Hilbert-Schmidt operators, finite rank perturbations of Volterra operators, infinite Leslie operators, discrete semi-separable operators, integral operators with semi-separable kernels, and period maps corresponding to delay differential equations. The classes of unbounded operators that are investigated appear in a natural way in the study of infinite dimensional dynamical systems such as mixed type functional differential equations, age-dependent population dynamics, and in the analysis of the Markov semigroup connected to the recently introduced zig-zag process..
出版日期Book 2022
关键词Completeness of the Linear Span of Eigenvectors; Characteristic Matrix Function; Trace Class and Hilbe
版次1
doihttps://doi.org/10.1007/978-3-031-04508-0
isbn_softcover978-3-031-04510-3
isbn_ebook978-3-031-04508-0Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Finite Rank Perturbations of Volterra Operators,ists of three sections. In the first section the characteristic matrix function is defined. The main theorem is a completeness theorem which is proved in the second section. In the final session we show that the results of the first two sessions remain true if the Volterra operator is replaced by a
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Periodic Delay Equations,a preliminary character and concern time dependent delay equations and the associated fundamental solutions. In the third section we show that a time dependent delay equation has an associated two parameter family of solution operators. In the last section of this chapter we introduce the period map
发表于 2025-3-22 20:28:16 | 显示全部楼层
Completeness Theorems for Period Maps,acting on Banach spaces of continuous functions. In the first section we show that these period maps are compact operators which can be written as the sum of a Volterra operator and a finite rank operator. The significance of completeness theorems for period maps is explained in the second and third
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Applications to Dynamical Systems,chotomous operators that appear in the study of functional differential equations. In the second section, we consider the infinitesimal generator of the semigroup associated with age-dependent population models. In the third section, we consider unbounded operators that arise in the study of Markov
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