In this note we show that for an arbitrary reductive Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles and show that they always lie along translates of walls of Weyl chambers.

MSC Classifications:

11F30, 22E30, 11F70, 22E45 show english descriptions Fourier coefficients of automorphic forms
Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Representation-theoretic methods; automorphic representations over local and global fields
Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 11F30 - Fourier coefficients of automorphic forms
22E30 - Analysis on real and complex Lie groups [See also 33C80, 43-XX]
11F70 - Representation-theoretic methods; automorphic representations over local and global fields
22E45 - Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}

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