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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...

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