Research Interests

Approximation theory and geometric methods in analysis, shape-preserving approximation, measures of smoothness and approximation, relations to other areas of analysis (geometry of Banach spaces, harmonic analysis, Fourier analysis) and mathematics (graph theory), convexity, computational and numerical methods, some problems in quantum information theory (perfect state transfer, mutually unbiased bases).

Seminar

Approximation Theory, Applications and Related Topics seminar

Research Grants

Holding NSERC Discovery Grant "Multivariate Approximation".

Presentations

  • On Nikol'skii inequalities for domains in R^d download pdf watch video (Oaxaca, Mexico, June 2015)
  • Non-existence of (76,30,8,14) strongly regular graph and some structural tools (short version) download pdf (Saskatoon, Canada, June 2015)
  • Non-existence of (76,30,8,14) strongly regular graph and some structural tools (long version) download pdf (Winnipeg, Canada, March 2015)
  • Discrete d-dimensional moduli of smoothness download pdf (Sevastopol, Ukraine, June 2013)
  • Geometry of Banach spaces and sharp versions of Jackson and Marchaud inequalities download pdf (Ein-Gedi, Israel, January 2012)

Publications

  • A. V. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, M. Viazovska, There is no strongly regular graph with parameters (460,153,32,60), preprint download (arXiv)
  • A. Bondarenko, A. Prymak, D. Radchenko, Non-existence of (76,30,8,14) strongly regular graph and some structural tools, preprint 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 R^d, Constructive Approximation, 44 (2016) 23-51 download (arXiv) view Springer's version through ReadCube
  • O. Maizlish, A. Prymak, Convex polynomial approximation in 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 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
  • 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 Lp, 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