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.
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© 2010 Birkhäuser / Springer Basel AG
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Graf, U. (2010). Mellin Transforms. In: Introduction to Hyperfunctions and Their Integral Transforms. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0408-6_6
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DOI: https://doi.org/10.1007/978-3-0346-0408-6_6
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0407-9
Online ISBN: 978-3-0346-0408-6
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