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Bargmann representation of q-commutation relations for q > 1 and associated measures

Ilona Królak (2007)

Banach Center Publications

The classical Bargmann representation is given by operators acting on the space of holomorphic functions with the scalar product z | z k q = δ n , k [ n ] q ! = F ( z z ̅ k ) . We consider the problem of representing the functional F as a measure for q > 1. We prove the existence of such a measure and investigate some of its properties like uniqueness and radiality. The above problem is closely related to the indeterminate Stieltjes moment problem.

Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss

Laurence Halpern, Jeffrey Rauch (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

We analyse Bérenger’s split algorithm applied to the system version of the two dimensional wave equation with absorptions equal to Heaviside functions of x j , j = 1 , 2 . The methods form the core of the analysis [11] for three dimensional Maxwell equations with absorptions not necessarily piecewise constant. The split problem is well posed, has no loss of derivatives (for divergence free data in the case of Maxwell), and is perfectly matched.

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