### 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. Arman, A. Bondarenko, A. Prymak, D. Radchenko, Upper bounds on chromatic number of $\mathbb{E}^n$ in low dimensions, download (arXiv) data and scripts (github)
• A. Prymak, Every 3-dimensional convex body can be covered by 14 smaller homothetic copies, pre-print, download (arXiv) data and scripts (github)
• A. Bondarenko, A. Prymak, D. Radchenko, Spherical coverings and X-raying convex bodies of constant width, Canad. Math. Bull., 2021, 1-7. doi:10.4153/S0008439521001016 download (arXiv)
• F. Dai, A. Prymak, $L^p$-Bernstein inequalities on $C^2$-domains, Trans. Amer. Math. Soc., accepted on Aug. 23 2021, download (arXiv)
• A. Prymak, Geometric computation of Christoffel functions on planar convex domains, Journal of Approximation Theory, 268 (2021), 105603, download (arXiv)
• F. Dai, A. Prymak, A. Shadrin, V. Temlyakov, S. Tikhonov, Entropy numbers and Marcinkiewicz-type discretization theorem, Journal of Functional Analysis, 281 (2021), 109090, doi:10.1016/j.jfa.2021.109090, download (arXiv)
• F. Dai, A. Prymak, On directional Whitney inequality, Canadian Journal of Mathematics, 2021, 1-25. doi:10.4153/S0008414X21000110 download (arXiv)
• F. Dai, A. Prymak, A. Shadrin, V. Temlyakov, S. Tikhonov, Sampling discretization of integral norms, Constructive Approximation, 54 (2021), 455-471 ,download (arXiv)
• F. Dai, A. Prymak, Polynomial approximation on $C^2$-domains, pre-print, download (arXiv) [this pre-print is being divided into three separate publications]
• A. Prymak, V. Shepelska, On the Hadwiger covering problem in low dimensions, Journal of Geometry, 111 42 (2020), 1-11, download (arXiv) view Springer's version through ReadCube
• A. Prymak, O. Usoltseva, Pointwise behavior of Christoffel function on planar convex domains, in: Topics in Classical and Modern Analysis. In Memory of Yingkang Hu, Birkhauser, 2019, 293-302, download (arXiv)
• F. Dai, A. Prymak, V.N. Temlyakov, S. Tikhonov, Integral norm discretization and related problems, Uspekhi Matematicheskikh Nauk, 74 (2019), no. 4 (448), 3-58 [in Russian], translated to English in: Russian Math. Surveys 74 (2019), no. 4, 579-630, download English version (arXiv)
• A. Prymak, O. Usoltseva, Christoffel function on planar domains with piecewise smooth boundary, Acta Math. Hungar., 158 (2019), no. 1, 216-234, download (arXiv) view Springer's version through ReadCube
• 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. 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
• K. Kopotun, D. Leviatan, A. V. Prymak, Constrained spline smoothing, SIAM Journal on Numerical Analysis, 46 (2008), no. 4, 1985-1997 download (arXiv) download pdf (© SIAM)
• Z. Ditzian, A. V. Prymak, Ul'yanov-type inequality for bounded convex sets in Rd, Journal of Approximation Theory, 151 (2008), no. 1, 60-85
• Z. Ditzian, A. Prymak, Sharp Marchaud and converse inequalities in Orlicz spaces, Proceedings of the American Mathematical Society, 135 (2007) 1115-1121
• K. Kopotun, D. Leviatan, A. V. Prymak, Nearly monotone spline approximation in Lp, Proceedings of the American Mathematical Society, 134 (2006) 2037-2047
• D. Leviatan, A. V. Prymak, On 3-monotone approximation by piecewise polynomials, Journal of Approximation Theory, 133 (2005) 147-172
• A. V. Prymak, Smoothing of 3-convex splines of 4-th degree with shape preservation, Ukrainian Mathematical Journal, 57 2 (2005) 277-283 [in Ukrainian]
• A. V. Bondarenko, A. V. Prymak, Negative results in high-order shape preserving approximation, Matematicheskie Zametki, 76 6 (2004) 812-823 [in Russian], translated in Mathematical Notes, 76 6 (2004) 758-769
• A. V. Bondarenko, A. V. Prymak, Convex multivariate approximation by algebras of continuous functions, Proceedings of International Conference "Advances in Constructive Approximation" (USA), 2004, 123-131 download (arXiv)
• A. V. Prymak, Three-convex approximation by quadratic splines with arbitrary fixed knots, East Journal on Approximations, 8 2 (2002) 185-196