### Research Interests

Analysis, approximation theory, combinatorics, convex geometry, numerical analysis.

### Research Grants

Holding NSERC Discovery Grant "Multivariate Approximation".

### Publications

(some pre-prints of these articles can be found at Research Gate)
• A. Prymak, V. Shepelska, On illumination of the boundary of a convex body in $\mathbb{E}^n$, $n=4,5,6$, pre-print, download (arXiv)
• A. Prymak, O. Usoltseva, Christoffel function on planar domains with piecewise smooth boundary, pre-print, download (arXiv)
• F. Dai, A. Prymak, V.N. Temlyakov, S. Tikhonov, Integral norm discretization and related problems, pre-print, download (arXiv)
• S. Brodiuk, N. Palko, A. Prymak, On Banach-Mazur distance between planar convex bodies, Aequationes Mathematicae, 92 (2018), 993-1000, download (arXiv) view Springer's version through ReadCube
• A. Prymak, O. Usoltseva, Pointwise behavior of Christoffel function on planar convex domains, accepted in special volume of the International conference on approximation theory dedicated to the memory of Y. Xu, download (arXiv)
• A. V. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, M. Viazovska, There is no strongly regular graph with parameters (460,153,32,60), Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Wozniakowski, eds.), Springer-Verlag (2018), 131-134 download (arXiv)
• A. Prymak, Upper estimates of Christoffel function on convex domains, Journal of Mathematical Analysis and Applications, 455 (2017) 1984-2000, download (arXiv)
• A. Bondarenko, A. Prymak, D. Radchenko, Non-existence of (76,30,8,14) strongly regular graph, Linear Algebra and its Applications, 527 (2017) 53-72 download (arXiv), supplementary files
• K. A. Kopotun, D. Leviatan, A. Prymak, I. A. Shevchuk, Yet another look at positive linear operators, q-monotonicity and applications, Journal of Approximation Theory, 210 (2016) 1-22 download (arXiv)
• Z. Ditzian, A. Prymak, On Nikol'skii inequalities for domains in $\mathbb{R}^d$, Constructive Approximation, 44 (2016) 23-51 download (arXiv) view Springer's version through ReadCube
• O. Maizlish, A. Prymak, Convex polynomial approximation in $\mathbb{R}^d$ with Freud weights, Journal of Approximation Theory, 192 (2015) 60--68 download (arXiv)
• Z. Ditzian, A. Prymak, Discrete d-dimensional moduli of of smoothness, Proc. Amer. Math. Soc., 142 (2014), no. 10, 3553-3559 download (arXiv)
• A. Bondarenko, A. Prymak, D. Radchenko, On concentrators and related approximation constants, J. Math. Anal. Appl., 402 (2013) 234-241 download (arXiv)
• A. Bondarenko, D. Leviatan, A. Prymak, Pointwise estimates for 3-monotone approximation, Journal of Approximation Theory, 164 (2012) 1205-1232
• K. A. Kopotun, D. Leviatan, A. Prymak, I. A. Shevchuk, Uniform and pointwise shape preserving approximation by algebraic polynomials, Surv. Approx. Theory, 6 (2011), 24-74 download (arXiv)
• Z. Ditzian, A. Prymak, Convexity, moduli of smoothness and a Jackson-type inequality, Acta Math. Hung., 130 (2011), no. 3, 254-285 download (arXiv)
• Z. Ditzian, A. Prymak, Extension technique and estimates for moduli of smoothness on domains in $\mathbb{R}^d$, East J. Approx., 17 (2011), no. 2, 127-135
• G. Dzyubenko, K. Kopotun, A. Prymak, Three-monotone spline approximation, Journal of Approximation Theory, 162 (2010), 2168-2183
• Z. Ditzian, A. Prymak, Approximation by dilated averages and K-functionals, Canadian Journal of Mathematics, 62 (2010), no. 4, 737-757 download (open access from CMS)
• Z. Ditzian, A. Prymak, Nikol'skii inequalities for Lorentz spaces, Rocky Mountain Journal of Mathematics, 40 (2010), no. 1, 209-223
• K. Kopotun, D. Leviatan, A. V. Prymak, Nearly monotone and nearly convex approximation by smooth splines in $L_p$, $p>0$, Journal of Approximation Theory, 160 (2009), 103-112