Dirac’S Delta Function Hausdorff Dimension Function Pair of Reciprocal Functions Due to the Theorem by Mellin 44A05 46F12 28A78
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 7, No 4, (2004), 409p-420p
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.