On a convolution property characterizing the Laguerre functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On a convolution property characterizing the Laguerre functions

Authors:	Georg Budke

Affiliation:	(1) Gesellschaft für Strahlen- und Umweltforschung, Medis Institut, Ingolstädter Landstrasse 1, D-8042 Neuherberg, Federal Republic of Germany

Abstract:	Consider the Laguerre functions $l_n^p (t) = ( - 1)^n sqrt {2p} L_n (2p t)e^{ - pt}$ (with parameterp>0), where theL_n are the Laguerre polynomials with parameter =0.{l_n^p(t)}_n=0 forms a complete orthonormal system inL² ([0, )). A well known and often used property of the Laguerre functions is the convolution property: $sqrt {2p} l_i^p * l_j^p = l_{i + j}^p + l_{i + j + 1}^p$ for alli,j0. It is the objectiveof this note that the system of Laguerre functions is the only complete and orthonormal system ofL² ([0, )) satisfying the convolution property.

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