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Convergence of Taylor series in Fock spaces

Haiying Li (2014)

Studia Mathematica

It is well known that the Taylor series of every function in the Fock space F α p converges in norm when 1 < p < ∞. It is also known that this is no longer true when p = 1. In this note we consider the case 0 < p < 1 and show that the Taylor series of functions in F α p do not necessarily converge “in norm”.

Counting walks in a quadrant: a unified approach via boundary value problems

Kilian Raschel (2012)

Journal of the European Mathematical Society

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations...

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