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

Opened Access The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function
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Autor: Berg, Christian
Durán Guardeño, Antonio José
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2008
Publicado en: Mathematica Scandinavica, 103 (1), 11-39.
Tipo de documento: Artículo
Resumen: We study the fixed point for a non-linear transformation in the set of Hausdorff moment sequences, defined by the formula: T ((an))n = 1/(a0+···+an). We determine the corresponding measureμ, which has an increasing and convex density on ]0, 1[, and we study some analytic functions related to it. The Mellin transform F of μ extends to a meromorphic function in the whole complex plane. It can be characterized in analogy with the Gamma function as the unique log-convex function on ]−1,∞[ satisfying F (0) = 1 and the functional equation 1/F (s) = 1/F (s + 1) − F (s + 1), s > −1.
Cita: Berg, C. y Durán Guardeño, A.J. (2008). The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function. Mathematica Scandinavica, 103 (1), 11-39.
Tamaño: 211.6Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43393

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