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ISSN 1088-6826(e) ISSN 0002-9939(p)

A note on generating functions for Hausdorff moment sequences

Author(s): Oliver Roth; Stephan Ruscheweyh; Luis Salinas
Journal: Proc. Amer. Math. Soc. 136 (2008), 3171-3176.
MSC (2000): Primary 30E05, 26A48
Posted: April 30, 2008
MathSciNet review: 2407081
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Abstract | References | Similar articles | Additional information

Abstract: For functions whose Taylor coefficients at the origin form a Hausdorff moment sequence we study the behaviour of $w(y):=\vert f(\gamma+iy)\vert$ for ( $\gamma\leq1$ fixed).

References:

1.: W.B. Donoghue Jr., Monotone matrix functions and analytic continuation, Grundlehren Math. Wiss. 207, Springer-Verlag (1974). MR 0486556 (58:6279)
2.: F. Hausdorff, Summationsmethoden und Momentfolgen I, Math. Z. 9 (1921), 74-109. MR 1544453
3.: S. Ruscheweyh, Nichtlineare Extremalprobleme für holomorphe Stieltjesintegrale, Math. Z. 142 (1975), 19-23. MR 0374406 (51:10606)
4.: S. Ruscheweyh, L. Salinas, and T. Sugawa, Completely monotone sequences and universally prestarlike functions, preprint 2007.
5.: K.J. Wirths, Über totalmonotone Zahlenfolgen, Arch. Math. 26 (1975), 508-517. MR 0396930 (53:790)

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Additional Information:

Oliver Roth
Affiliation: Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
Email: roth@mathematik.uni-wuerzburg.de

Stephan Ruscheweyh
Affiliation: Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
Email: ruscheweyh@mathematik.uni-wuerzburg.de

Luis Salinas
Affiliation: Departamento de Informática, Universidad Técnica F. Santa María, Valparaíso, Chile
Email: lsalinas@inf.utfsm.cl

DOI: 10.1090/S0002-9939-08-09460-4
PII: S 0002-9939(08)09460-4
Keywords: Hausdorff moment sequences, completely monotone sequences, Pick functions, convolution, polylogarithms
Received by editor(s): July 5, 2007
Posted: April 30, 2008
Additional Notes: The first and second authors acknowledge partial support from the German-Israeli Foundation (grant G-809-234.6/2003). The second and third authors received partial support from FONDECYT (grants 1070269 and 7070131) and DGIP-UTFSM (grant 240721).
Communicated by: Andreas Seeger
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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