Search results for "C0-semigroup"
showing 10 items of 25 documents
Explicit solutions for second-order operator differential equations with two boundary-value conditions. II
1992
AbstractBoundary-value problems for second-order operator differential equations with two boundary-value conditions are studied for the case where the companion operator is similar to a block-diagonal operator. This case is strictly more general than the one treated in an earlier paper, and it provides explicit closed-form solutions of boundary-value problem in terms of data without increasing the dimension of the problem.
Operator martingale decomposition and the Radon-Nikodym property in Banach spaces
2010
Abstract We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon–Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney–Schaefer l-tensor product E ⊗ ˜ l Y , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon–Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E ⊗ ˜ l Y . Secondly, we derive a Riesz decomposition for uniform …
Boundaries for algebras of analytic functions on function module Banach spaces
2013
We consider the uniform algebra of continuous and bounded functions that are analytic on the interior of the closed unit ball of a complex Banach function module X. We focus on norming subsets of , i.e., boundaries, for such algebra. In particular, if X is a dual complex Banach space whose centralizer is infinite-dimensional, then the intersection of all closed boundaries is empty. This also holds in case that X is an -sum of infinitely many Banach spaces and further, the torus is a boundary.
Sur une classe d’equations du type parabolique lineaires
1996
The application of the variational method for the existence theorem, developped by J. L. Lions, for the evolution equations in Hilbert spaces to a considerably large class of systems of linear partial differential equations of parabolic type is studied by defining Hilbert spaces in relation to the elliptic operator of the system, and an example insired by the system of equations for a viscous gas is examined.
Regularity of solutions to differential equations with non-Lipschitz coefficients
2008
AbstractWe study the ordinary and stochastic differential equations whose coefficients satisfy certain non-Lipschitz conditions, namely, we study the behaviors of small subsets under the flows generated by these equations.
Continuous *-homomorphisms of Banach Partial *-algebras
2007
We continue the study of Banach partial *-algebras, in particular the question of the interplay between *-homomorphisms and biweights. Two special types of objects are introduced, namely, relatively bounded biweights and Banach partial *-algebras satisfying a certain Condition (S), which behave in a more regular way. We also present a systematic construction of Banach partial *-algebras of this type and exhibit several examples.
Dissipative operators and differential equations on Banach spaces
1991
If we consider the initial value problem Inline Equation $$x'(t) = f(t,x(t)),{\text{ }}x(0) = {x_0}$$ on the real line, it is well known that one—sided bounds like Inline Equation $$\left[ {f(t,x) - f\left( {t,y} \right)} \right]\left( {x - {\text{y}}} \right) \leqslant \omega {\left( {x - y} \right)^2}$$ give much better information about the behaviour of solutions than the Lipschitz- type estimates Inline Equation $$ \left| {f\left( {t,x} \right) - f\left( {t,y} \right)} \right| \leqslant L\left| {x - y} \right|,$$ because ω, unlike L, may be negative.
Common fixed point results on quasi-Banach spaces and integral equations
2013
In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations.
Asymptotic Equivalence of Difference Equations in Banach Space
2014
Conjugacy technique is applied to analysis asymptotic equivalence of nonautonomous linear and semilinear difference equations in Banach space.
Domains of accretive operators in Banach spaces
2016
LetD(A)be the domain of anm-accretive operatorAon a Banach spaceE. We provide sufficient conditions for the closure ofD(A)to be convex and forD(A)to coincide withEitself. Several related results and pertinent examples are also included.