Completeness Theorems and Characteristic Matrix Functions : Applications to Integral and Differential Operators
2022 ed.
Book Details
Format
Hardback or Cased Book
ISBN-10
3031045076
ISBN-13
9783031045073
Edition
2022 ed.
Publisher
Birkhauser Verlag AG
Imprint
Birkhauser Verlag AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jun 14th, 2022
Print length
350 Pages
Product Classification:
Functional analysis & transforms Differential calculus & equations
Ksh 21,600.00
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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.
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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