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pro vyhledávání: '"Sitnik, S. M."'
Autor:
Sitnik, S. M.
In this preprint we consider generalizations of discrete and integral Cauchy--Bunyakovskii inequalities by the method of mean values with some applications. Mostly the material is compiled as a short survey but some results are proved. Main results a
Externí odkaz:
http://arxiv.org/abs/2203.14344
Publikováno v:
Lobachevskii Journal Of Mathematics 41:3 (2020) 423-429
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations by linear
Externí odkaz:
http://arxiv.org/abs/2007.02694
Autor:
Shishkina, E. L., Sitnik, S. M.
This is a survey paper in two parts. In the first part we list main variants of one-dimensional fractional integrodifferential operators. Also some historical and priority remarks are given. As a special question we consider the impact of Soviet and
Externí odkaz:
http://arxiv.org/abs/2006.09893
Akademický článek
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Autor:
Katrakhov, V. V., Sitnik, S. M.
Publikováno v:
Contemporary Mathematics. Fundamental Directions. 64:2 (2018) 211-428
The main content of this book is composed from two doctoral theses: by V.\,V.~Katrakhov (1989) and by S.\,M.~Sitnik (2016). In our work, for the first time in the format of a monograph, we systematically expound the theory of transmutation operators
Externí odkaz:
http://arxiv.org/abs/1809.10887
Autor:
Sitnik, S. M., Shishkina, E. L.
Publikováno v:
Siberian Electronic Mathematical Reports, 15 (2018) 1--10
In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre functions f
Externí odkaz:
http://arxiv.org/abs/1706.01928
Autor:
Shishkina, E. L., Sitnik, S. M.
Publikováno v:
Journal of Inequalities and Special Functions 8:1 (2017)49-67
This paper was published in the special issue of the Journal of Inequalities and Special Functions dedicated to Professor Ivan Dimovski's contributions to different fields of mathematics: transmutation theory, special functions, integral transforms,
Externí odkaz:
http://arxiv.org/abs/1703.02232
Autor:
Sitnik, S. M.
Publikováno v:
Journal of Inequalities and Special Functions 8:1 (2017) 140-157
This paper was published in the special issue of the Journal of Inequalities and Special Functions dedicated to Professor Ivan Dimovski's contributions to different fields of mathematics: transmutation theory, special functions, integral transforms,
Externí odkaz:
http://arxiv.org/abs/1703.02228
Autor:
Pevnyi, A. B., Sitnik, S. M.
Publikováno v:
Journal Of Mathematical Sciences (Springer) 205:2 (2015) 304-307
We consider a new and simpler proof of an inequality of A.S. Gasparyan, which was originally derived in terms of complex algebraical objects --- multidimensional hyperdeterminants. Our proof is much simpler and use only standard technics such as mean
Externí odkaz:
http://arxiv.org/abs/1609.01249
Autor:
Pevnyi, A. B., Sitnik, S. M.
We investigate inequalities of M.G. Krein, Yu.V. Linnik and E.A. Gorin for positive definite functions. Modifications and generalizations of these inequalities are proved. We also prove that multipoint E.A. Gorin's inequality follows from two--point
Externí odkaz:
http://arxiv.org/abs/1609.01218