Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 24.01.1961
E-mail: ,
Keywords: inequalities, integral operators, transmutations, special functions, numerical methods, approximation of functions.
UDC: 517.926.4, 517.968.25

Subject:

1. Transmutation operators.
2. Integral operators with special function kernels.
3. Classical inequalities.
4. Special functions and their inequalities.

Main publications:

1. Elina Shishkina, Sergei Sitnik, Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics, Mathematics in Science and Engineering, Elsevier. Academic Press, 2020 , 592 pp. https://www.elsevier.com/books/transmutations-singular-and-fractional-differential-equations-with-applications-to-mathematical-physics/shishkina/978-0-12-819781-3        
2. V. V. Kravchenko, S. M. Sitnik, Transmutation Operators and Applications, Trends in Mathematics, eds. Kravchenko, Vladislav, Sitnik, Sergei M., Birkhauser, Springer Nature Switzerland AG, Basel, 2020 , XVII, 686 pp. https://www.springer.com/gp/book/9783030359133        
3. S. M. Sitnik, E. L. Shishkina, Metod operatorov preobrazovaniya dlya differentsialnykh uravnenii s operatorami Besselya, Fizmatlit, Moskva, 2019 , 224 pp.
4. Valeriy V. Katrakhov, Sergey M. Sitnik, “Transmutation Method and Boundary-Value Problems for Singular Elliptic Equations”, English translation by Professor A.B.Muravnik, arxiv.org, 2022, 1–207 https://doi.org/10.48550/arXiv.2210.02246        
5. S.M. Sitnik, A.S. Timashov, S.N. Ushakov, “On the Correctness of Finite-Rank Approximations by Series of Shifted Gaussians”, Lobachevskii Journal Of Mathematics, 41:3 (2020), 423-429 https://link.springer.com/article/10.1134/S1995080220030166, arXiv: 2007.02694            
6. Fitouhi A., Jebabli I., Shishkina E.L., Sitnik S.M., “Applications of integral transforms composition method to wave-type singular differential equations and index shift transmutations”, Electron. J. Differential Equations, 2018 (2018), 130 , 27 pp. https://ejde.math.txstate.edu/Volumes/2018/130/abstr.html, arXiv: https://arxiv.org/abs/1805.06925}{https://arxiv.org/abs/1805.06925}          
7. S. M. Sitnik, Kh. Mehrez, “Proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions”, Analysis (De Gruyter), 36:4 (2016), 263–268 https://www.degruyter.com/view/j/anly.2016.36.issue-4/anly-2015-0029/anly-2015-0029.xml?format=INT        
8. S.M. Sitnik, Generalized Young and Cauchy-Bunyakowsky Inequalities with Applications: a survey, 2010 , 51 pp., arXiv: arXiv:1012.3864  
9. D.Karp, S.M.Sitnik, “Log-convexity and log-concavity of hypergeometric-like functions”, Journal of Mathematical Analysis and Applications, 364 (2010), P. 384-–394. , arXiv: 0902.3073v1          
10. Sitnik S.M., “Inequalities for Bessel functions”, Dokl. Math. of the Russian Academy of Sciences, 51:1 (1995), 25–28        
11. S. M. Sitnik, “Faktorizatsiya i otsenki norm v vesovykh lebegovykh prostranstvakh operatorov Bushmana–Erdeii”, (predstavlena akademikom S. M. Nikolskim), Doklady Akademii Nauk SSSR, 320:6 (1991), 1326–1330        ; S. M. Sitnik, “Factorization and estimates of the norms of Buschman-Erdelyi operators in weighted Lebesgue spaces”, Soviet Mathematics Doklades. Soviet Academy of Sciences,, 44:2 (1992), 641–646    
12. Katrakhov V.V., Sitnik S.M., “A boundary–value problem for the steady-state Schrodinger equation with a singular potential”, Soviet Math. Dokl., 30:2 (1984), 468–470            

Recent publications

Presentations in Math-Net.Ru

Personal pages:

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Organisations:

• Voronezh State University
• Voronezh Polytechnic Institute
• Institute for Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok
• Far-Eastern State Technical University, Vladivostok
• Voronezh Institute of Russian Ministry of Internal Affairs
• National Research University "Belgorod State University"