A sufficient condition for the Carasso-Kato theorem.
A sufficient condition for the Carasso-Kato theorem (Erratum).
A symbolic calculus and a parametrix construction for pseudodifferential operators with non-smooth negative definite symbols.
A theorem of Rolewicz's type for measurable evolution families in Banach spaces.
A universal property of -semigroups
Let be a -semigroup with unbounded generator . We prove that has generically a very irregular behaviour for as .
A viability result for nonconvex semilinear functional differential inclusions
We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.
Absorption semigroups and Dirichlet boundary conditions.
Abstract formulation of an age-physiology dependent population dynamics problem
Abstract methods in differential equations.
This is an expanded version, enriched by references, of my inaugural speech held on November 7, 2001 at the Real Academia de Ciencas Exactas, Físicas y Naturales in Madrid. It explains in a nontechnical way, accessible to a general scientific community, some of the motivation and basic ideas of my research of the last twenty years on a functional-analytical approach to nonlinear parabolic problems.
Abstract multiplication semigroups.
Adjoint bi-continuous semigroups and semigroups on the space of measures
For a given bi-continuous semigroup on a Banach space we define its adjoint on an appropriate closed subspace of the norm dual . Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology . We give the following application: For a Polish space we consider operator semigroups on the space of bounded, continuous functions (endowed with the compact-open topology) and on the space of bounded Baire measures (endowed with the weak-topology)....
Admissibilité de l'observation pour des systèmes bilinéaires contrôlés par des opérateurs non bornés
Admissible and regular potentials for positive Co-semigroups and application to heat semigroups.
Almost automorphic functions with values in -Fréchet spaces.
Almost automorphy of semilinear parabolic evolution equations.
Almost periodic and strongly stable semigroups of operators
This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators on a Banach space X (discrete one-parameter semigroups), one-parameter -semigroups on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family of bounded...
Almost periodic solutions of higher order differential equations on Hilbert spaces.
Almost periodicity of C-semigroups, integrated semigroups and C-cosine functions
We investigate the characterization of almost periodic C-semigroups, via the Hille-Yosida space Z₀, in case of R(C) being non-dense. Analogous results are obtained for C-cosine functions. We also discuss the almost periodicity of integrated semigroups.
An Algebraic Approach to Implicit Evolution Equations
A Banach algebra homomorphism on the convolution algebra of integrable functions is the essence of Kisyński's equivalent formulation of the Hille-Yosida theorem for analytic semigroups. For the study of implicit evolution equations the notion of empathy happens to be more appropriate than that of semigroup. This approach is based upon the intertwining of two families of evolution operators and two families of pseudo-resolvents. In this paper we show that the Kisyński approach can be adapted to empathy...
An averaging principle for stochastic evolution equations. II.
In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.