Weighted inversion of general Dirichlet series

Inversion theorems of Wiener type are essential tools in analysis and number theory. We derive a weighted version of an inversion theorem of Wiener type for general Dirichlet series from that of Edwards from 1957, and we outline an alternative proof based on the duality theory of convex cones and ex...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2014-06, Vol.366 (6), p.3275-3293
Main Authors: Glöckner, Helge, Lucht, Lutz G.
Format: Article
Language:English
Subjects:
Absolute convergence
Algebra
Banach algebra
Commutativity
Homomorphisms
Mathematical functions
Mathematical theorems
Research article
Semigroups
Series convergence
Weighting functions
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Summary:Inversion theorems of Wiener type are essential tools in analysis and number theory. We derive a weighted version of an inversion theorem of Wiener type for general Dirichlet series from that of Edwards from 1957, and we outline an alternative proof based on the duality theory of convex cones and extension techniques for characters of semigroups. Variants and arithmetical applications are described, including the case of multidimensional weighted generalized Dirichlet series.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-2013-06018-7