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Hermite Series with Polar Singularities

Boychev, Georgi S. (2012)

Mathematica Balkanica New Series

MSC 2010: 33C45, 40G05Series in Hermite polynomials with poles on the boundaries of their regions of convergence are considered.

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...

I and I * -convergence in topological spaces

Benoy Kumar Lahiri, Pratulananda Das (2005)

Mathematica Bohemica

We extend the idea of I -convergence and I * -convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.

I-convergence theorems for a class of k-positive linear operators

Mehmet Özarslan (2009)

Open Mathematics

In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.

Ideal version of Ramsey's theorem

Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2011)

Czechoslovak Mathematical Journal

We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations shown in [P....

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