On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin
Norbert Südland, Gerd Baumann · Bulgarian Digital Mathematics Library (BulDML) at IMI-BAS (Institute of Mathematics and Informatics) · 2004
We prove that Dirac's (symmetrical) delta function and the Hausdorff dimension function build up a pair of reciprocal functions.Our reasoning is based on the theorem by Mellin.Applications of the reciprocity relation demonstrate the merit of this approach.