The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function | Zendy

Christian Berg | Zendy; Antonio J. Durán | Zendy

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The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function

Author(s) -

Christian Berg,

Antonio J. Durán

Publication year - 2008

Publication title -

mathematica scandinavica

Language(s) - English

Resource type - Journals

eISSN - 1903-1807

pISSN - 0025-5521

DOI - 10.7146/math.scand.a-15066

Subject(s) - mathematics , meromorphic function , hausdorff measure , transformation (genetics) , convex function , moment (physics) , regular polygon , function (biology) , hausdorff space , combinatorics , pure mathematics , mathematical analysis , hausdorff dimension , geometry , biochemistry , chemistry , physics , classical mechanics , evolutionary biology , biology , gene

We study the fixed point for a non-linear transformation in the set of Hausdorffmoment sequences,defined by the formula: T ((an))n = 1/(a0+E E E+an).We determine the corresponding measureE,which has an increasing and convex density on ]0, 1[, and we study some analytic functions relatedto it. TheMellin transform F of E extends to ameromorphic function in the whole complex plane.It can be characterized in analogy with the Gamma function as the unique log-convex functionon ].1,[ satisfying F(0) = 1 and the functional equation 1/F (s) = 1/F (s + 1) . F(s + 1),s > .1.

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