# Kolmogorov's problem about the existence of absolute monotone and multiply monotone functions with given norms of derivatives

 Title Kolmogorov's problem about the existence of absolute monotone and multiply monotone functions with given norms of derivatives Publication Type Journal Article Year of Publication 2015 Authors Babenko, VF, Babenko, Yu.V, Kovalenko, OV Abbreviated Key Title Dopov. Nac. akad. nauk Ukr. DOI 10.15407/dopovidi2015.10.007 Issue 10 Section Mathematics Pagination 7-11 Date Published 10/2015 Language Ukrainian Abstract Kolmogorov's problem about the existence of a function with given norms of derivatives for classes of multiply monotone functions and absolute monotone functions in the case of an arbitrary number of norms is solved. The connection of Kolmogorov's problem with Markov's moment problem is shown. Keywords absolute monotone function, inequalities for derivatives, Kolmogorov's problem, multiply monotone function
References:
1. Babenko V. F., Babenko Yu. V., Kovalenko O. V. Dopov. Nac. akad. nauk Ukr., 2013, No 11: 7–12 (in Russian).
2. Bernshtein S. N. Absolute monotone functions, Collection of works, Vol. 1, Moscow: Izd-vo AN SSSR, 1928 (in Russian).
3. Williamson R. E. Duke Math. J., 1956, 23, No 2: 189–207. https://doi.org/10.1215/S0012-7094-56-02317-1
4. Karlin S., Studden W. J. Tchebycheff systems with applications in analysis and statistics, New York: Interscience, 1966.
5. Krein M. G., Nudelman A. A. The Markov moment problem and extremal problems, Moscow: Fizmatlit, 1973 (in Russian).