Search results for "C0-semigroup"
showing 10 items of 25 documents
Property (w) and perturbations
2007
A bounded linear operator T ∈ L(X) defined on a Banach space X satisfies property (w), a variant of Weyl’s theorem, if the complement in the approximate point spectrum σa(T ) of the Weyl essential approximate spectrum σwa(T ) coincides with the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property (w), for a bounded operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operator and quasi-nilpotent operators commuting with T .
Incomparable Banach spaces and operator semigroups
2002
Using the notions of total incomparability and total coincomparability of Banach spaces, we define two families of operator semigroups. We show that these semigroups are minimal, in the sense that they admit a perturbative characterization. Moreover, they allow us to characterize the corresponding incomparability classes.
Infinite Dimensional Banach spaces of functions with nonlinear properties
2010
The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on R(n) failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.
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.
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.
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.
Partial differential equations governed by accretive operators
2012
The theory of nonlinear semigroups in Banach spaces generated by accretive operators has been very useful in the study of many nonlinear partial differential equations Such a theory is fundamentally based in the Crandall-Liggett Theorem and in the contributions of Ph. Benilan. In this paper, after outlining some of the main points of this theory, we present some of the applications to some nonlinear partial differential equations that appear in different fields of Science.
On lifting the approximation property from a Banach space to its dual
2014
A Noncommutative Approach to Ordinary Differential Equations
2005
We adapt ideas coming from Quantum Mechanics to develop a non-commutative strategy for the analysis of some systems of ordinary differential equations. We show that the solution of such a system can be described by an unbounded, self-adjoint and densely defined operator H which we call, in analogy with Quantum Mechanics, the Hamiltonian of the system. We discuss the role of H in the analysis of the integrals of motion of the system. Finally, we apply this approach to several examples.
A C0-Semigroup of Ulam Unstable Operators
2020
The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t&ge