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Summable families in nuclear groups

Wojciech Banaszczyk (1993)

Studia Mathematica

Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.

Summation of series via Laplace transforms.

Anthony Sofo (2002)

Revista Matemática Complutense

We consider a forced differential difference equation and by the use of Laplace Transform Theory generate non-hypergeometric type series which we prove may be expressed in closed form.

Summation processes viewed from the Fourier properties of continuous unimodular functions on the circle

Jean-Pierre Kahane (2011)

Banach Center Publications

The main purpose of this article is to give a new method and new results on a very old topic: the comparison of the Riemann processes of summation (R,κ) with other summation processes. The motivation comes from the study of continuous unimodular functions on the circle, their Fourier series and their winding numbers. My oral presentation in Poznań at the JM-100 conference exposed the ways by which this study was developed since the fundamental work of Brézis and Nirenberg on the topological degree...

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