Geodesic
Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an ``angle''
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2015), pp. 3-22

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For functions of two variables we obtain sharp inequalities of Kolmogorov's type for partial and mixed intermediate derivatives. We also consider applications of the results to some problems of approximation of functions of two variables by angles and obtain a series of relations which are exact in definite sense.
Keywords: Hermite polynomials, Fourier–Hermite series, inequalities of Kolmogorov's type, the best approximation by angle, generalized polynomial. 
@article{IVM_2015_11_a0,
     author = {S. B. Vakarchuk and A. V. Shvachko},
     title = {Inequalities of {Kolmogorov's} type for derived functions in two variables and application to approximation by an ``angle''},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--22},
     publisher = {mathdoc},
     number = {11},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_11_a0/}
}
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S. B. Vakarchuk; A. V. Shvachko. Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an ``angle''. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2015), pp. 3-22. http://geodesic.mathdoc.fr/item/IVM_2015_11_a0/