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On the Mellin transforms of Dirac’s delta function, the Hausdorff dimension function, and the theorem by Mellin. (English) Zbl 1106.44300

Summary: 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.

MSC:

44A05 General integral transforms
46F12 Integral transforms in distribution spaces
28A78 Hausdorff and packing measures
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