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On generalized absolutely monotone functions

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Abstract

Sufficient conditions for generalized absolutely monotone functions to possess a Taylor-type expansion in terms of the corresponding Extended Tchebycheff systems were found by Karlin and Ziegler. The question of necessary conditions, however, was left open. In this paper we solve this question by finding necessary and sufficient conditions for the validity of the expansion. The structure of the cone of generalized absolutely monotone functions and its extreme rays are also discussed.

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References

  1. S. Karlin and W. J. Studden,Tchebycheff Systems: with Applications in Analysis and Statistics, Interscience, New York, 1966.

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  2. S. Karlin and Z. Ziegler,Generalized absolutely monotone functions, Israel J. Math.3 (1965), 173–180.

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Authors and Affiliations

  1. Tel Aviv University, Israel

    D. Amir & Z. Ziegler

  2. Technion—Israel Institute of Technology, Haifa

    D. Amir & Z. Ziegler

Authors
  1. D. Amir
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  2. Z. Ziegler
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Additional information

The research of the second author was partially supported by U.S. Army Contract-DA-31-124-ARO-D-462 in the MRC, Madison, Wisconsin.

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Amir, D., Ziegler, Z. On generalized absolutely monotone functions. Israel J. Math. 7, 137–146 (1969). https://doi.org/10.1007/BF02771660

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  • DOI: https://doi.org/10.1007/BF02771660

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