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A function related to a Lagrange-Bürmann series

Paul Bracken (2002)

Czechoslovak Mathematical Journal

An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.

A lower bound on the radius of analyticity of a power series in a real Banach space

Timothy Nguyen (2009)

Studia Mathematica

Let F be a power series centered at the origin in a real Banach space with radius of uniform convergence ϱ. We show that F is analytic in the open ball B of radius ϱ/√e, and furthermore, the Taylor series of F about any point a ∈ B converges uniformly within every closed ball centered at a contained in B.

Accelero-summation of the formal solutions of nonlinear difference equations

Geertrui Klara Immink (2011)

Annales de l’institut Fourier

In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level 1 + ”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum...

An elementary proof of the Briançon-Skoda theorem

Jacob Sznajdman (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function φ belongs to an ideal I of the ring of germs of analytic functions at 0 n ; more precisely, the ideal membership is obtained if a function associated with φ and I is locally square integrable. If I can be generated by m elements,it follows in particular that I min ( m , n ) ¯ I , where J ¯ denotes the integral closure of an ideal J .

Approximation de fonctions holomorphes d'un nombre infini de variables

László Lempert (1999)

Annales de l'institut Fourier

Soit X un espace de Banach complexe, et notons B ( R ) X la boule de rayon R centrée en 0 . On considère le problème d’approximation suivant: étant donnés 0 < r < R , ϵ > 0 et une fonction f holomorphe dans B ( R ) , existe-t-il toujours une fonction g , holomorphe dans X , telle que | f - g | < ϵ sur B ( r ) ? On démontre que c’est bien le cas si X est l’espace l 1 des suites sommables.

Approximation of holomorphic functions of infinitely many variables II

László Lempert (2000)

Annales de l'institut Fourier

Let X be a Banach space and B ( R ) X the ball of radius R centered at 0 . Can any holomorphic function on B ( R ) be approximated by entire functions, uniformly on smaller balls B ( r ) ? We answer this question in the affirmative for a large class of Banach spaces.

Diagonal series of rational functions (several variables)

Sławomir Cynk, Piotr Tworzewski (1994)

Annales Polonici Mathematici

We give representations of Nash functions in a neighbourhood of a polydisc (torus) in m as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in m + 1 .

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