Geodesic
On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin
Fractional calculus and applied analysis, Tome 7 (2004) no. 4, pp. 409-420.

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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.
Keywords: Dirac’S Delta Function, Hausdorff Dimension Function, Pair of Reciprocal Functions Due to the Theorem by Mellin, 44A05, 46F12, 28A78 
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Südland, Norbert; Baumann, Gerd. On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin. Fractional calculus and applied analysis, Tome 7 (2004) no. 4, pp. 409-420. http://geodesic.mathdoc.fr/item/FCAA_2004_7_4_a2/