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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Solution of the Karlin problem for zero-diminishing sequences satisfying a Carleman condition


Authors: Andrew Bakan and Stephan Ruscheweyh
Journal: Proc. Amer. Math. Soc. 136 (2008), 2665-2674
MSC (2000): Primary 12D10, 26C10, 30E05; Secondary 30C15, 30D15
Published electronically: March 27, 2008
MathSciNet review: 2399027
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Abstract: We describe all zero-diminishing sequences (over the real-valued polynomials on $ \mathbb{R}$) which additionally satisfy a Carleman condition and show that they are of the same kind as those in E. Laguerre's theorem from 1884.


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Additional Information

Andrew Bakan
Affiliation: Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska Street 3, Kyiv 01601, Ukraine
Email: andrew@bakan.kiev.ua

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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09256-3
PII: S 0002-9939(08)09256-3
Keywords: Zero-diminishing sequences, moment problems, zeros of polynomials
Received by editor(s): October 28, 2005
Received by editor(s) in revised form: April 10, 2007
Published electronically: March 27, 2008
Additional Notes: This work was completed while A. Bakan was visiting Würzburg University, supported by the German Academic Exchange Service (DAAD, grant 322-A/02/12977). S. Ruscheweyh acknowledges partial support from the German-Israeli Foundation (grant G-809-234.6/2003)
Communicated by: David Preiss
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.