Laguerre expansions and products of distributions
Commun. Korean Math. Soc. 2008 Vol. 23, No. 2, 201-209
Printed June 1, 2008
Pedro Catuogno, Federico Martinez, and Sandra Molina
Universidade Estadual de Campinas, Universidad Nacional de Mar del Plata, and Universidad Nacional de Mar del Plata
Abstract : In this paper we introduce two products of tempered distributions with positive support. These products are based in the Laguerre representation of distributions. We calculate some products as, $[\delta] x_{+}^{\lambda}=\delta [ x_{+}^{\lambda}]=0$ and $[ x_{+}^{\lambda}]x_{+}^{\mu}=x_{+}^{\lambda+\mu}$ for appropriate $\lambda$ and $\mu$.
Keywords : product of distributions, tempered distributions with positive support, Laguerre functions
MSC numbers : 46F10, 42C10
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