Data dependence for Ishikawa iteration when dealing with contractive-like operators.
Data dependence for some integral equation via weakly Picard operators.
Decay of solutions of some nonlinear equations.
Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity
This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation , by means of regularly varying functions, where is a positive constant and is a positive continuous function on . It is shown that if is a regularly varying function, then it is possible to establish necessary and sufficient conditions for the existence of slowly varying solutions and regularly varying solutions of (A) which decrease to as and to acquire...
Decoherence of quantum Markov semigroups
Decomposability of Cylindrical Martingales and Absolutely Summing Operators.
Decomposability of extremal positive unital maps on M₂(ℂ)
A map φ: Mₘ(ℂ) → Mₙ(ℂ) is decomposable if it is of the form φ = φ₁ + φ₂ where φ₁ is a CP map while φ₂ is a co-CP map. It is known that if m = n = 2 then every positive map is decomposable. Given an extremal unital positive map φ: M₂(ℂ) → M₂(ℂ) we construct concrete maps (not necessarily unital) φ₁ and φ₂ which give a decomposition of φ. We also show that in most cases this decomposition is unique.
Decomposability of operator-valued functions
Decomposable embeddings, complete trajectories, and invariant subspaces
We produce closed nontrivial invariant subspaces for closed (possibly unbounded) linear operators, A, on a Banach space, that may be embedded between decomposable operators on spaces with weaker and stronger topologies. We show that this can be done under many conditions on orbits, including when both A and A* have nontrivial non-quasi-analytic complete trajectories, and when both A and A* generate bounded semigroups that are not stable.
Decomposable hulls of multifunctions
Let F be a multifunction with values in Lₚ(Ω, X). In this note, we study which regularity properties of F are preserved when we consider the decomposable hull of F.
Decomposable multipliers and applications to harmonic analysis
For a multiplier on a semisimple commutative Banach algebra, the decomposability in the sense of Foiaş will be related to certain continuity properties and growth conditions of its Gelfand transform on the spectrum of the multiplier algebra. If the multiplier algebra is regular, then all multipliers will be seen to be decomposable. In general, an important tool will be the hull-kernel topology on the spectrum of the typically nonregular multiplier algebra. Our investigation involves various closed...
Decomposable subspaces of Banach spaces.
We introduce and study the notion of hereditarily A-indecomposable Banach space for A a space ideal. For a hereditarily A-indecomposable space X we show that the operators from X into a Banach space Y can be written as the union of two sets A Φ+(X,Y) and A(X;Y ). For some ideals A defined in terms of incomparability, the first set is open, the second set correspond to a closed operator ideal and the union is disjoint.
Decomposable systems of differential operators and generalized inverses
Decomposing and twisting bisectorial operators
Bisectorial operators play an important role since exactly these operators lead to a well-posed equation u'(t) = Au(t) on the entire line. The simplest example of a bisectorial operator A is obtained by taking the direct sum of an invertible generator of a bounded holomorphic semigroup and the negative of such an operator. Our main result shows that each bisectorial operator A is of this form, if we allow a more general notion of direct sum defined by an unbounded closed projection. As a consequence...
Decomposition and disintegration of positive definite kernels on convex *-semigroups
The paper deals with operator-valued positive definite kernels on a convex *-semigroup whose Kolmogorov-Aronszajn type factorizations induce *-semigroups of bounded shift operators. Any such kernel Φ has a canonical decomposition into a degenerate and a nondegenerate part. In case is commutative, Φ can be disintegrated with respect to some tight positive operator-valued measure defined on the characters of if and only if Φ is nondegenerate. It is proved that a representing measure of a positive...
Décomposition atomique des espaces de Bergman.
The aim of this paper is to establish the theorem of atomic decomposition of weighted Bergman spaces Ap(Ω), where Ω is a domain of finite type in C2. We construct a kernel function H(z,w) which is a reproducing kernel for Ap(Ω) and we prove that the associated integral operator H is bounded in Lp(Ω).
Decomposition conditions for two-point boundary value problems.
Décomposition et classification des systèmes dynamiques
Decomposition of homogeneous vector fields of degree one and representation of the flow
Decomposition of operators with countable spectrum.
Sufficient spectral conditions for the existence of a spectral decomposition of an operator T defined on a Banach space X, with countable spectrum, are given. We apply the results to obtain the West decomposition of certain Riesz operators.