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Polina Yu. Glazyrina

Polina Yu. Glazyrina
Ural Federal University, Ekaterinburg, Russian Federation

Institute of Natural Sciences and Mathematics

Department of Mathematical Analysis, Associate Professor, Leading Mathematician 

PhD (Phys., Math.)

ScopusID: 8716323000

ResearcherID: O-1511-2017

ORCID ID: 0000-0002-7733-3220

Scientific interests: Theory of functions

Scientific achievements: The main scientific interests are connected with the study of properties of polynomials and their derivatives. The sharp Markov inequalities for derivatives of algebraic polynomials on an interval for Lq, L0 metrics, the sharp Bernstein-Szego inequality for fractional derivatives of trigonometric polynomials for Lq, L∞ metrics and its analogs for more general operators and integral functionals, Turan’s inequality for convex domains of complex plains, Ulyanov-type inequalities for Ditzian–Totik moduli of smoothness are obtained.

Main publications:

  1. Glazyrina P.Yu. The Markov Brothers Inequality in L0-Space on an Interval // Mathematical Notes, 2005. Vol. 78, no. 1. P. 53-58. DOI:10.1007/s11006-005-0098-8
  2. Glazyrina P.Yu. The sharp Markov-Nikol’skii inequality for algebraic polynomials in the spaces Lq and L0 on a closed interval // Mathematical Notes, 2008. Vol. 84, no. 1–2. P. 3–21. DOI: 10.1134/S0001434608070018
  3. Glazyrina P.Yu. Necessary conditions for metrics in integral Bernstein-type inequalities // Journal of Approximation Theory, 2010. Vol. 162, no. 6. P. 1204–1210. DOI: 10.1016/j.jat.2009.12.009
  4. Arestov V.V. and Glazyrina P.Yu. Sharp integral inequalities for fractional derivatives of trigonometric polynomials // Journal of Approximation Theory, 2012. Vol. 164. P. 1501–1512. DOI: 10.1016/j.jat.2012.08.004
  5. Glazyrina P., Tikhonov S. Jacobi weights, fractional integration, and sharp Ulyanov inequalities // Journal of Approximation Theory. 2015. Vol. 195. P. 122–140. DOI: 10.1016/j.jat.2014.05.005
  6. Glazyrina P.Yu., Szegő–Taikov Inequality for Conjugate Polynomials // Comput. Methods Funct. Theory, 2015. Vol. 15, no. 4. P. 595–603.  DOI: 10.1007/s40315-015-0130-2
  7. Glazyrina P.Y., Ŕevesz S.G. Turán type oscillation inequalities in Lq norm on the boundary of convex domains // Mathematical Inequalities and Applications, 2017. Vol. 20, no. 1. P. 149–180. DOI: 10.7153/mia-20-11