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Approximation of entire functions of slow growth on compact sets

G. S. Srivastava, Susheel Kumar (2009)

Archivum Mathematicum

In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.

Approximation of holomorphic functions in Banach spaces admitting a Schauder decomposition

Francine Meylan (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let X be a complex Banach space. Recall that X admits afinite-dimensional Schauder decompositionif there exists a sequence { X n } n = 1 of finite-dimensional subspaces of X , such that every x X has a unique representation of the form x = n = 1 x n , with x n X n for every n . The finite-dimensional Schauder decomposition is said to beunconditionalif, for every x X , the series x = n = 1 x n , which represents x , converges unconditionally, that is, n = 1 x π ( n ) converges for every permutation π of the integers. For short, we say that X admits an unconditional F.D.D.We...

Continuous transformation groups on spaces

K. Spallek (1991)

Annales Polonici Mathematici

A differentiable group is a group in the category of (reduced and nonreduced) differentiable spaces. Special cases are the rationals ℚ, Lie groups, formal groups over ℝ or ℂ; in general there is some mixture of those types, the general structure, however, is not yet completely determined. The following gives as a corollary a first essential answer. It is shown, more generally,that a locally compact topological transformation group, operating effectively on a differentiable space X (which satisfies...

Croissance des fonctions plurisousharmoniques en dimension infinie

Christer O. Kiselman (1984)

Annales de l'institut Fourier

Les ensembles polaires dans C n , c’est-à-dire les ensembles où une fonction plurisousharmonique qui n’est pas - identiquement admet cette valeur, apparaissent comme des ensembles exceptionnels dans beaucoup de problèmes en analyse complexe. Par exemple, la croissance d’une fonction plurisousharmonique en une variable y quand une autre variable x est fixée est essentiellement la même pour tout x sauf quand x appartient à un ensemble polaire. Dans l’article un résultat très précis et général de cette...

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