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Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity

Ivana Kučerová (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation x ' ' ' + q ( t ) x - γ = 0 , by means of regularly varying functions, where γ is a positive constant and q is a positive continuous function on [ a , ) . It is shown that if q 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 0 as t and to acquire...

Decomposability of extremal positive unital maps on M₂(ℂ)

Władysław A. Majewski, Marcin Marciniak (2006)

Banach Center Publications

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.

Decomposable embeddings, complete trajectories, and invariant subspaces

Ralph deLaubenfels, Phóng Vũ (1996)

Studia Mathematica

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

Andrzej Nowak, Celina Rom (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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

Kjeld Laursen, Michael Neumann (1992)

Studia Mathematica

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...

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