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A Dichotomy Principle for Universal Series

V. Farmaki, V. Nestoridis (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence ( α j ) j = 1 of scalars, there exists a subsequence ( α k j ) j = 1 such that either every subsequence of ( α k j ) j = 1 defines a universal series, or no subsequence of ( α k j ) j = 1 defines a universal series. In particular examples we decide which of the two cases holds.

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.

Approximation by p -Faber-Laurent rational functions in the weighted Lebesgue spaces

Daniyal M. Israfilov (2004)

Czechoslovak Mathematical Journal

Let L C be a regular Jordan curve. In this work, the approximation properties of the p -Faber-Laurent rational series expansions in the ω weighted Lebesgue spaces L p ( L , ω ) are studied. Under some restrictive conditions upon the weight functions the degree of this approximation by a k th integral modulus of continuity in L p ( L , ω ) spaces is estimated.

Closed universal subspaces of spaces of infinitely differentiable functions

Stéphane Charpentier, Quentin Menet, Augustin Mouze (2014)

Annales de l’institut Fourier

We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace...

Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem

B. Jakubczyk (2000)

Annales Polonici Mathematici

We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.

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