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Completeness Theorems and Characteristic Matrix Functions
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Completeness Theorems and Characteristic Matrix Functions
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.
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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.
Produktdetaljer
Sprog: Engelsk
Sider: 350
ISBN-13: 9783031045073
Indbinding: Hardback
Udgave:
ISBN-10: 3031045076
Udg. Dato: 14 jun 2022
Længde: 0mm
Bredde: 235mm
Højde: 155mm
Oplagsdato: 14 jun 2022
Forfatter(e) Sjoerd M. Verduyn Lunel, Marinus A. Kaashoek


Kategori Funktionsanalyse og transformation


Sprog Engelsk


Indbinding Hardback


Sider 350


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm

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