Characteristic Matrices and Spectral Properties of Evolutionary Systems

DOI10.2307/2154470zbMath0768.34041OpenAlexW4255918397MaRDI QIDQ4032462

Sjoerd M. Verduyn Lunel, Marinus A. Kaashoek

Publication date: 1 April 1993

Full work available at URL: https://doi.org/10.2307/2154470

zbMATH Keywords

Banach spaceinfinite delayinfinitesimal generatorneutral functional differential equationshyperbolic systemJordan chaindifferential-difference equationcharacteristic matrixunbounded closed linear operatorage- dependent population dynamical models

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) General theory of functional-differential equations (34K05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items (20)

Spectral theory for structured perturbations of linear operators ⋮ Large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order ⋮ Unnamed Item ⋮ Series expansions for functional differential equations ⋮ Stability and control of feedback systems with time delays ⋮ Linearly similar Szökefalvi-Nagy–Foias model in a domain ⋮ Spectral analysis of the zigzag process ⋮ On the dominance of roots of characteristic equations for neutral functional differential equations ⋮ A functional model approach to linear neutral functional differential equations ⋮ Characteristic matrix functions for delay differential equations with symmetry ⋮ On equivalence and linearization of operator matrix functions with unbounded entries ⋮ Spectrum-based Stability Analysis and Stabilization of Time-periodic Time-delay Systems ⋮ Center manifolds for periodic functional differential equations of mixed type ⋮ Functional differential equation with infinite delay in a space of exponentially bounded and uniformly continuous functions ⋮ Center projections for smooth difference equations of mixed type ⋮ Accumulation of complex eigenvalues of a class of analytic operator functions ⋮ Projectors on the generalized eigenspaces for functional differential equations using integrated semigroups ⋮ Geometric invariance of determining and resonating centers: Odd- and any-number limitations of Pyragas control ⋮ Characteristic matrix functions and periodic delay equations ⋮ Bifurcation analysis of systems with delays: methods and their use in applications

Cites Work

• Factorization of matrix and operator functions. The state space method
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• Spectral properties of finite-dimensional perturbed linear semigroups
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• Root functions of boundary eigenvalue operator functions
• Linearization of boundary eigenvalue problems
• Classes of linear operators. Vol. I
• Linear autonomous neutral functional differential equations
• On autonomous linear functional differential equations with infinite retardations
• Equivalence, linearization, and decomposition of holomorphic operator functions
• A multiplicity theorem for hyperbolic systems
• Functional differential equations with infinite delays
• A folk theorem in functional differential equations
• Linear Functional Differential Equations as Semigroups on Product Spaces
• The Largest Class of Hereditary Systems Defining a C₀ Semigroup on the Product Space
• Generalized Jordan chains and two bifurcation theorems of Krasnoselskii
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