Completeness and F-completeness of eigenfunctions associated with retarded functional differential equations
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Publication:1253005
DOI10.1016/0022-0396(80)90045-5zbMath0395.47017OpenAlexW1970581644MaRDI QIDQ1253005
Publication date: 1980
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-0396(80)90045-5
Groups and semigroups of linear operators (47D03) General theory of functional-differential equations (34K05) Linear differential equations in abstract spaces (34G10) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)
Related Items (27)
State space theory of linear time invariant systems with delays in state, control, and observation variables. I, II ⋮ Pointwise completeness and degeneracy of functional differential equations in Banach spaces. I: General time delays ⋮ Finite-dimensional regulators for a class of infinite-dimensional systems ⋮ Characterization of small solutions in functional differential equations ⋮ A note on spectral realisations for delay systems ⋮ Density of images of semigroup operators for linear neutral functional differential equations ⋮ The structure of the singularities of holomorphic matrices ⋮ The structural operator F and its role in the theory of retarded systems ⋮ The structural operator F and its role in the theory of retarded systems. II ⋮ Spectral properties of the operator associated with a retarded functional differential equation in Hilbert space ⋮ Series expansions and small solutions for Volterra equations of convolution type ⋮ Unnamed Item ⋮ Functional-differential equations in Sobolev spaces and related problems of spectral theory ⋮ Identification problems of retarded differential systems in Hilbert spaces ⋮ Parameter identifiability of differential delay equations ⋮ Control problems for semi-linear retarded integro-differential equations by the Fredholm theory ⋮ Invariant manifolds for singularly perturbed linear functional differential equations ⋮ Finite dimensional representation of distributed delay systems ⋮ F-reduction of the operator Riccati equation for hereditary differential systems ⋮ Structure theory and duality for the time varying retarded functional differential equations ⋮ On the regularity of solutions of an operator Riccati equation arising in linear quadratic optimal control problems for hereditary differential systems ⋮ A unified approach to constrained approximate controllability for the heat equations and the retarded equations ⋮ On structured distance to uncontrollability of general linear retarded systems ⋮ Observability of nontrivial small solutions for neutral systems ⋮ On approximate and exact null controllability of delay systems ⋮ Approximate controllability of linear retarded systems in Hilbert spaces ⋮ A sharp version of Henry's theorem on small solutions
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