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A universal property of C 0 -semigroups

Gerd Herzog, Christoph Schmoeger (2009)

Commentationes Mathematicae Universitatis Carolinae

Let T : [ 0 , ) L ( E ) be a C 0 -semigroup with unbounded generator A : D ( A ) E . We prove that ( T ( t ) x - x ) / t has generically a very irregular behaviour for x D ( A ) as t 0 + .

A viability result for nonconvex semilinear functional differential inclusions

Vasile Lupulescu, Mihai Necula (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

Abstract methods in differential equations.

Herbert Amann (2003)

RACSAM

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.

Adjoint bi-continuous semigroups and semigroups on the space of measures

Bálint Farkas (2011)

Czechoslovak Mathematical Journal

For a given bi-continuous semigroup ( T ( t ) ) t 0 on a Banach space X we define its adjoint on an appropriate closed subspace X of the norm dual X ' . Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ ( X , X ) . We give the following application: For Ω a Polish space we consider operator semigroups on the space C b ( Ω ) of bounded, continuous functions (endowed with the compact-open topology) and on the space M ( Ω ) of bounded Baire measures (endowed with the weak * -topology)....

Almost periodic and strongly stable semigroups of operators

Vũ Phóng (1997)

Banach Center Publications

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 T n : n = 0 , 1 , . . . on a Banach space X (discrete one-parameter semigroups), one-parameter C 0 -semigroups T ( t ) : t 0 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...

An Algebraic Approach to Implicit Evolution Equations

Wha-Suck Lee, Niko Sauer (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

Bohdan Maslowski, Jan Seidler, Ivo Vrkoč (1991)

Mathematica Bohemica

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.

Currently displaying 41 – 60 of 86