Südland, Norbert; Baumann, Gerd On the Mellin transforms of Dirac’s delta function, the Hausdorff dimension function, and the theorem by Mellin. (English) Zbl 1106.44300 Fract. Calc. Appl. Anal. 7, No. 4, 409-420 (2004). 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. Cited in 2 Documents MSC: 44A05 General integral transforms 46F12 Integral transforms in distribution spaces 28A78 Hausdorff and packing measures Keywords:pair of reciprocal functions; Dirac’s delta function; Hausdorff dimension function PDFBibTeX XMLCite \textit{N. Südland} and \textit{G. Baumann}, Fract. Calc. Appl. Anal. 7, No. 4, 409--420 (2004; Zbl 1106.44300) Full Text: EuDML