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On the functions whose inverse is jet-absolutely monotonic. (English) Zbl 1028.26006

Summary: The infinitely differentiable real-valued functions whose inverse have all the Taylor coefficients nonnegative at the fixed-point of the axis are considered. An application to the theory of the inverse pair of the Radon measures is given.

MSC:

26A48 Monotonic functions, generalizations
26E10 \(C^\infty\)-functions, quasi-analytic functions
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References:

[1] Dieudonne J., Infinitesimal Calculus (1971)
[2] Riordan J., An Introduction To Combinatorial Analysis (1958) · Zbl 0078.00805
[3] Widder D.V., The Laplace Transform (1941) · Zbl 0063.08245
[4] DOI: 10.1007/BF02592679 · JFM 55.0142.07 · doi:10.1007/BF02592679
[5] DOI: 10.1214/aos/1176347491 · Zbl 0714.62010 · doi:10.1214/aos/1176347491
[6] Seshadri V., The inverse Gaussian distribution (1993)
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