Displaying similar documents to “Spaces of D-paraanalytic elements”

Overstability and resonance

Augustin Fruchard, Reinhard Schäfke (2003)

Annales de l’institut Fourier

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We consider a singularity perturbed nonlinear differential equation ε u ' = f ( x ) u + + ε P ( x , u , ε ) which we suppose real analytic for x near some interval [ a , b ] and small | u | , | ε | . We furthermore suppose that 0 is a turning point, namely that x f ( x ) is positive if x 0 . We prove that the existence of nicely behaved (as ϵ 0 ) local (at x = 0 ) or global, real analytic or C solutions is equivalent to the existence of a formal series solution u n ( x ) ε n with u n analytic at x = 0 . The main tool of a proof is a new “principle of analytic continuation” for...

Solutions of non-homogeneous linear differential equations in the unit disc

Ting-Bin Cao, Zhong-Shu Deng (2010)

Annales Polonici Mathematici

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The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + + a ( z ) f ' + a ( z ) f = F ( z ) , where all coefficients a , a , . . . , a k - 1 , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.

Algebraic and analytic properties of solutions of abstract differential equations

R. Bittner

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CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions....................................................................................................................................

Co-analytic, right-invertible operators are supercyclic

Sameer Chavan (2010)

Colloquium Mathematicae

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Let denote a complex, infinite-dimensional, separable Hilbert space, and for any such Hilbert space , let () denote the algebra of bounded linear operators on . We show that for any co-analytic, right-invertible T in (), αT is hypercyclic for every complex α with | α | > β - 1 , where β i n f | | x | | = 1 | | T * x | | > 0 . In particular, every co-analytic, right-invertible T in () is supercyclic.

The Lindelöf property and σ-fragmentability

B. Cascales, I. Namioka (2003)

Fundamenta Mathematicae

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In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space [ - 1 , 1 ] D is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of [ - 1 , 1 ] D is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is...

On the group of real analytic diffeomorphisms

Takashi Tsuboi (2009)

Annales scientifiques de l'École Normale Supérieure

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The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the n -dimensional torus, its identity component is a simple group. For U ( 1 ) fibered manifolds, for manifolds admitting special semi-free U ( 1 ) actions and for 2- or 3-dimensional manifolds with nontrivial U ( 1 ) actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.

Persistence of fixed points under rigid perturbations of maps

Salvador Addas-Zanata, Pedro A. S. Salomão (2014)

Fundamenta Mathematicae

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Let f: S¹ × [0,1] → S¹ × [0,1] be a real-analytic diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift f̃: ℝ × [0,1] → ℝ × [0,1] we have Fix(f̃) = ℝ × 0 and that f̃ positively translates points in ℝ × 1. Let f ̃ ϵ be the perturbation of f̃ by the rigid horizontal translation (x,y) ↦ (x+ϵ,y). We show that F i x ( f ̃ ϵ ) = for all ϵ > 0 sufficiently small. The proof follows from Kerékjártó’s construction of Brouwer lines for orientation preserving...