Research Interests

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

Research Grants

Holding NSERC Discovery Grant "Multivariate Approximation".

Presentations

Publications

(some pre-prints of these articles can be found at Research Gate)
  • A. Arman, A. Bondarenko, A. Prymak, Convex bodies of constant width with exponential illumination number, pre-print, download (arXiv)
  • F. Dai, A. Kroo, A. Prymak, On Bernstein- and Marcinkiewicz-type inequalities on multivariate $C^\alpha$-domains, pre-print, download (arXiv)
  • 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, J. Singh, Whitney-type estimates for convex functions, Pure and Applied Functional Analysis, Special Issue on Approximation Theory and Related Topics dedicated to Professor Dany Leviatan on the occasion of his 80th birthday, accepted on Jan. 1 2024, download (arXiv)
  • F. Dai, A. Prymak, Polynomial approximation on $C^2$-domains, Constructive Approximation, accepted on Sept. 27, 2023, download (arXiv) view Springer's version through ReadCube
  • F. Dai, A. Prymak, Optimal polynomial meshes exist on any multivariate convex domain, Foundations of Computational Mathematics, accepted on Nov. 21 2022. download (arXiv) view Springer's version through ReadCube
  • F. Dai, A. Prymak, A. Shadrin, V. Temlyakov, S. Tikhonov, On cardinality of the lower sets and universal discretization, Journal of Complexity, 76 (2023), 101726. download (arXiv)
  • A. Prymak, A new bound for Hadwiger's covering problem in $\mathbb{E}^3$, SIAM J. Discrete Math., 37 no. 1 (2023), 17-24. download (arXiv) data and scripts (github)
  • F. Dai, A. Prymak, $L^p$-Bernstein inequalities on $C^2$-domains and applications to discretization, Trans. Amer. Math. Soc., 375 no. 3 (2022), 1933-1976, download (arXiv)
  • F. Dai, A. Prymak, On directional Whitney inequality, Canadian Journal of Mathematics, 74 (3) 2022, 833-857. doi:10.4153/S0008414X21000110 download (arXiv)
  • A. Bondarenko, A. Prymak, D. Radchenko, Spherical coverings and X-raying convex bodies of constant width, Canad. Math. Bull., 65 (4) 2022, 860-866. doi:10.4153/S0008439521001016 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, 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