Abstract
The problem we consider here is under what conditions analytic functions which are positive on a segment of the real axis can be expressed as ratios of two absolutely monotonic functions, that is, functions all of whose derivatives are non-negative on the given segment.
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References
Fraenkel, A.S. and Gordon, B. and Straus, E.G.: On the determination of sets by sets of sums of a certain order, Pacific J. Math. 12 (1962), 187–196.
Lambek, J. and Moser, L.: On some two way classifications of integers, Can. Math. Bull. 2 (1959), 85–89.
Motzkin, T.S. and Straus, E.G.: Divisors of polynomials and power series with positive coefficients, Pacific J. Math. 29 (1969), 641–652.
Polya, G.: Über positive Darstellung von Polynomen, Vierteljahvsschrift Zürich 73 (1928), 141–145.
Selfridge, J.L. and Straus, E.G.: On the determination of numbers by their sums of a fixed order, Pacific J. Math. 8 (1958), 847–856.
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Straus, E.G. (1973). Real Analytic Functions as Ratios of Absolutely Monotonic Functions. In: Meir, A., Sharma, A. (eds) Spline Functions and Approximation Theory. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 21. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5979-0_15
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DOI: https://doi.org/10.1007/978-3-0348-5979-0_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5980-6
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