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Holomorphic extensions of formal objects

Javier Ribón (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We are interested on families of formal power series in ( , 0 ) parameterized by n ( f ^ = m = 0 P m ( x 1 , , x n ) x m ). If every P m is a polynomial whose degree is bounded by a linear function ( d e g P m A m + B for some A > 0 and B 0 ) then the family is either convergent or the series f ^ ( c 1 , , c n , x ) { x } for all ( c 1 , , c n ) n except a pluri-polar set. Generalizations of these results are provided for formal objects associated to germs of diffeomorphism (formal power series, formal meromorphic functions, etc.). We are interested on describing the nature of the set of parameters where...

Hypercyclicity of convolution operators on spaces of entire functions

F.J. Bertoloto, G. Botelho, V.V. Fávaro, A.M. Jatobá (2013)

Annales de l’institut Fourier

In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables

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