Research Interests

My general interest is classical analysis -- approximations and expansions, abstract harmonic analysis, Fourier analysis, numerical approximation and computational geometry. Specifically, I worked on: shape-preserving approximation, measures of smoothness and approximation, spline approximation, multivariate approximation.

Publications

  • Z. Ditzian, A. Prymak, Convexity, moduli of smoothness and a Jackson-type inequality, Acta Mathematica Hungarica, accepted on May 31, 2010
  • 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
  • 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
  • A. V. Prymak, Three-convex approximation by quadratic splines with arbitrary fixed knots, East Journal on Approximations, 8 2 (2002) 185-196