On sequences of Dirichlet polynomials uniformly bounded on half planes
Identifieur interne : 002C21 ( Main/Curation ); précédent : 002C20; suivant : 002C22On sequences of Dirichlet polynomials uniformly bounded on half planes
Auteurs : M. Wiessner [Allemagne]Source :
- Periodica Mathematica Hungarica [ 0031-5303 ] ; 1993-06-01.
Abstract
Abstract: Given $$0 \leqslant \lambda _0< \lambda _1< \cdots< \lambda _n \to \infty $$ and a sequence of Dirichlet polynomials $$\tau _n (z) = \sum\limits_{v = 0}^n {a_{nv} e^{ - \lambda _v z} (a_{nv} \in C)} $$ estimates for the coefficientsa nν are proved if {τn} is uniformly bounded on a region containing a half plane. Thereby a result is obtained which is an analogue of a known result for polynomials, that is for theA-transforms of the geometric sequence; moreover a Jentzsch type theorem for {τn(z)} is derived.
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DOI: 10.1007/BF01875974
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