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

2007/02/15 by Christian Berg, Antonio J. Durán, Berg, Christian +1
Mathematics · #30D05 #44A60 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0702446

openalex publication_date 2007/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the fixed point for a non-linear transformation in the set of\n Hausdorff moment sequences, defined by the formula: T((a_n))_n=1/(a₀+...\n+a_n). We determine the corresponding measure \μ, which has an increasing\nand convex density on ]0,1[, and we study some analytic functions related to\nit. The Mellin transform F of \μ extends to a meromorphic function in the\nwhole complex plane. It can be characterized in analogy with the Gamma function\nas the unique log-convex function on ]-1,\∞[ satisfying F(0)=1 and the\nfunctional equation 1/F(s)=1/F(s+1)-F(s+1), s>-1.\n

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