Kolmogorov's problem about the existence of absolute monotone and multiply monotone functions with given norms of derivatives
DOI:
https://doi.org/10.15407/dopovidi2015.10.007Keywords:
absolute monotone function, inequalities for derivatives, Kolmogorov's problem, multiply monotone functionAbstract
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.
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Bernshtein S. N. Absolute monotone functions, Collection of works, Vol. 1, Moscow: Izd-vo AN SSSR, 1928 (in Russian).
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Krein M. G., Nudelman A. A. The Markov moment problem and extremal problems, Moscow: Fizmatlit, 1973 (in Russian).
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