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Mellin Transforms

In: Introduction to Hyperfunctions and Their Integral Transforms

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  • Urs Graf

Abstract

First, the classical Mellin transformation is introduced and the connection with the two-sided Laplace transformation is established. Several Mellin transforms of ordinary functions are then computed. In order to define the Mellin transform of a hyperfunction, the established connection with Laplace transformation is exploited. This connection is also used to establish all operational rules that govern the Mellin transformation. The two types of Mellin convolutions as well as the Mellin transform of a product and Parseval’s formula are then treated. Some simple applications conclude the chapter.

Suggested Citation

  • Urs Graf, 2010. "Mellin Transforms," Springer Books, in: Introduction to Hyperfunctions and Their Integral Transforms, chapter 0, pages 309-336, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0346-0408-6_6
    DOI: 10.1007/978-3-0346-0408-6_6
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