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Mellin Transforms of Multivariate Rational Functions

Lisa Nilsson (Institutionen för matematiska vetenskaper, matematik) ; M. Passare
Journal of Geometric Analysis (1050-6926). Vol. 23 (2013), 1, p. 24-46.
[Artikel, refereegranskad vetenskaplig]

This paper deals with Mellin transforms of rational functions g/f in several variables. We prove that the polar set of such a Mellin transform consists of finitely many families of parallel hyperplanes, with all planes in each such family being integral translates of a specific facial hyperplane of the Newton polytope of the denominator f. The Mellin transform is naturally related to the so-called coamoeba , where Z (f) is the zero locus of f and Arg denotes the mapping that takes each coordinate to its argument. In fact, each connected component of the complement of the coamoeba gives rise to a different Mellin transform. The dependence of the Mellin transform on the coefficients of f, and the relation to the theory of A-hypergeometric functions is also discussed in the paper.

Nyckelord: Mellin transform, Coamoeba, Hypergeometric function, hypergeometric-functions

Denna post skapades 2013-06-11. Senast ändrad 2016-11-07.
CPL Pubid: 178270


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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