Publications of K. Kopotun:

Note: some of the files may not be the very final versions of papers and may contain misprints corrected during proofreading of the galley proofs.

 

·       (with D. Leviatan and I. A. Shevchuk) Exact order of pointwise estimates for polynomial approximation with Hermite interpolation. (.pdf)

·       (with D. Leviatan, I. Petrova and I. A. Shevchuk) Interpolatory pointwise estimates for convex polynomial approximation. Acta Math. Hung.   (.pdf or arxiv.org version)

·        (with D. Leviatan and I. A. Shevchuk) Uniform and pointwise shape preserving approximation (SPA) by algebraic polynomials: an update. SMAI Journal of Computational Mathematics S5 (2019): 99-108. (.pdf or arxiv.org version)

·       (with D. Leviatan and I. A. Shevchuk) On one estimate of divided differences and its applications. Ukrainian Mathematical J. 71, 2 (2019): 230-245. (.pdf or arxiv.org version)

·       (with D. Leviatan and I. A. Shevchuk) On some properties of moduli of smoothness with Jacobi weights. Topics in Classical and Modern Analysis, Applied and Numerical Harmonic Analysis, Springer (2019): 19-31 (.pdf or arxiv.org version)

·        (with D. Leviatan and I. A. Shevchuk) Interpolatory estimates for convex piecewise polynomial approximation. Journal of Mathematical Analysis and Applications 474, 1 (2019): 467–479. (.pdf or arxiv.org version)

·       (with D. Leviatan and I. A. Shevchuk) On weighted approximation with Jacobi weights. J. of Approximation Theory 237 (2019): 96-112. (.pdf  or arxiv.org version)   

·       (with D. Leviatan and I. A. Shevchuk) On moduli of smoothness with Jacobi weights. Ukrainian Mathematical J. 70, 3 (2018):  379-403. (arxiv .pdf, published .pdf) (Note: A version of this paper in Ukrainian Math. J. 70 (2018), no. 3, 437-466 contains errors introduced by the journal while “translating” this paper from English to English.)

·       (with D. Leviatan and I. A. Shevchuk) Interpolatory pointwise estimates for monotone polynomial approximation. Journal of Mathematical Analysis and Applications 459, 2 (2018): 1260-1295. (.pdf or arxiv.org version)

·       (with D. Leviatan, A. Prymak and I. A. Shevchuk) Yet another look at positive linear operators, q-monotonicity and applications. J. of Approximation Theory 210 (2016): 1-22. (.pdf)

·       Uniform polynomial approximation with A* weights having finitely many zeros. Journal of Mathematical Analysis and Applications 435 (2016): 677-700. (.pdf)

·       (with D. Leviatan and I. A. Shevchuk) Constrained approximation with Jacobi weights. Canadian J. Math. 68, 1 (2016): 109-128. (.pdf)

·       Polynomial approximation with doubling weights having finitely many inner zeros and singularities. J. of Approximation Theory 198 (2015): 24-62.  (.pdf)   

·       Polynomial approximation with doubling weights. Acta Math. Hung. 146, 2 (2015): 496-535. (.pdf)

·       Weighted moduli of smoothness of k-monotone functions and applications. J. of Approximation Theory. 192 (2015): 102-131. (.pdf)

·       (with D. Leviatan and I. A. Shevchuk) New moduli of smoothness: weighted DT moduli revisited and applied. Constructive Approximation 42, 1 (2015): 129-159. (.pdf)

·       (with D. Leviatan and I. A. Shevchuk) New moduli of smoothness. Publications de l'Institut Mathématique (Beograd) 96 (110) (2014): 169-180. (.pdf)

·       (with D. Leviatan, A. Prymak and I. A. Shevchuk) Uniform and Pointwise Shape Preserving Approximation by Algebraic Polynomials. Surveys in Approximation Theory 6 (2011): 24-74. (.pdf)

·       (with G. Dzyubenko and A. Prymak) Three-monotone spline approximation. J. of Approximation Theory 162 (2010): 2168–2183. (.pdf)

·       (with D. Leviatan and I. Shevchuk) Are the degrees of best (co)convex and unconstrained polynomial approximation the same? II. Ukr. Mat. Zh. 62, 3 (2010): 369-386; Ukrainian Mathematical J. 62, 3 (2010): 420-440. (.pdf )

·       (with B. Popov) Moduli of Smoothness of Splines and Applications in Constrained Approximation. Jaen Journal on Approximation 2, 1 (2010): 79-91. (.pdf)

·       (with V. Konovalov and V. Maiorov) Convex Polynomial and Ridge Approximation of Lipschitz Functions in Rd. Rocky Mountain J. Math 40, 3 (2010): 957-976. (.pdf)

·       (with D. Leviatan and A. Prymak) Nearly Monotone and Nearly Convex Approximation by Smooth Splines in Lp, p > 0. J. of Approximation Theory 160 (2009): 103-112. (.pdf)

·       (with D. Leviatan and I. Shevchuk) Are the degrees of best (co)convex and unconstrained polynomial approximation the same? Acta Math. Hung. 123, 3 (2009): 273-290. (.pdf)

·       On moduli of smoothness of k-monotone functions and applications. Math. Proc. Cambridge Philos. Soc. 146 (2009): 213-223.  (.pdf)

·       (with D. Leviatan and A. Prymak) Constrained Spline Smoothing. SIAM J. Numer. Analysis 46, 4 (2008): 1985-1997. (.pdf)

·       (with V. N. Konovalov) Kolmogorov, Linear and Pseudo-Dimensional Widths of Classes of  s-monotone Functions in  Lp, 0<p<1. Canadian Math. Bulletin 51, 2 (2008): 236-248. (.pdf)

·       Univariate Splines: Equivalence of Moduli of Smoothness and Applications. Mathematics of Computation 76 (2007): 931-945. (.pdf)

·       (with D. Leviatan and A. Prymak) Nearly Monotone Spline Approximation in Lp.  Proc. Amer. Math. Soc. 134, 7 (2006), 2037-2047. (.pdf)

·       On Equivalence of Moduli of Smoothness of Splines in Lp, 0<p<1. J. of Approximation Theory 143, 1 (2006), 36-43. (.pdf)

·       (with D. Leviatan and I. Shevchuk) Coconvex Approximation in the Uniform Norm:  the Final Frontier. Acta Math. Hung. 110, 1–2 (2006), 117–151. (.pdf) (note: Figures 1 and 2 on page 122 did not print properly in the original published vesion; this page was reprinted by the journal in a later issue but does not appear online; the file on this page is the correct full version of this paper)

·       (with D. Leviatan and I. Shevchuk) Convex Polynomial Approximation in the Uniform Norm: Conclusion. Canadian J. Math. 57, 6 (2005): 1224-1248. (.pdf)

·       On k-monotone Interpolation. Advances in Constructive Approximation, Nashboro Press, M. Neamtu and E. B. Saff (eds.), (2004): 265-275. (.pdf)

·       (with A. Shadrin) On k-monotone approximation by free knot splines. SIAM J. Math. Analysis 34, 4 (2003): 901-924. (.pdf)

·       (with M. Neamtu and B. Popov) Weakly Nonoscillatory Schemes for Scalar Conservation Laws. Mathematics of Computation  72 (2003): 1747-1767. (.pdf)

·       Whitney theorem of interpolatory type for k-monotone functions. Constructive Approximation 17 (2001): 307-317 (.pdf)

·       (with Y. K. Hu and X. M. Yu) On Multivariate Adaptive Approximation. Constructive Approximation 16 (2000): 449-474. (.pdf)

·       (with Y. K. Hu and X. M. Yu) Modified Adaptive Algorithms. SIAM J. Numerical Analysis 38, 3 (2000): 1013-1033. (.pdf)

·       (with Y. K. Hu and X. M. Yu) Weak Copositive and Intertwining Approximation. J. of Approximation Theory 96 (1999): 213-236. (.pdf)

·       (with D. Leviatan and I. A. Shevchuk) The degree of coconvex polynomial approximation. Proc. Amer. Math. Soc. 127 (1999): 409-415. (.pdf)

·       Approximation of k-monotone functions. J. of Approximation Theory 94 (1998): 481-493. (.pdf)

·       (with D. Leviatan) Degree of Simultaneous Coconvex Polynomial Approximation. Result. Math. 34 (1998): 150-155. (.pdf)

·       (with D. Leviatan ) Comonotone polynomial approximation in Lp [-1, 1], 0<p≤∞.  Acta Math. Hungar. 77, 4 (1997): 301-310. (.pdf)

·       (with Y. K. Hu and X. M. Yu) Constrained Approximation in Sobolev Spaces. Canadian J. Math. 49 (1997): 74-99. (.pdf)

·       (with Y. K. Hu and X. M. Yu) On Positive and Copositive Polynomial and Spline Approximation in Lp [-1, 1], 0<p<∞.  J. of Approximation Theory 86, 3 (1996): 320-334. (.pdf)

·       A Note on the Convexity of the Sum of Subpermanents. Linear Algebra and its Applications 245 (1996): 157-169. (.pdf)

·       Simultaneous Approximation by Algebraic Polynomials. Constructive Approximation 12 (1996): 67-94. (.pdf)

·       On K-monotone Polynomial and Spline Approximation in Lp, 0<p<∞  (quasi)norm. Approximation Theory VIII, World Scientific Publishing Co., C. Chui and L. Schumaker (eds.), (1995): 295-302. (.pdf – preprint; .pdf – published)

·       On Copositive Approximation by Algebraic Polynomials. Analysis Mathematica 21 (1995): 269-283. (.pdf)

·       Coconvex Polynomial Approximation of Twice Differentiable Functions. J. of Approximation Theory 83 (1995): 141-156. (.pdf)

·       A Note on Simultaneous Approximation in Lp [-1, 1] (1≤p<∞). Analysis 15 (1995): 151-158. (.pdf)

·       Unconstrained and Convex Polynomial Approximation in C[-1,1]. Approx. Theory Appl. 11, 2 (1995): 41-58. (.pdf)

·       Uniform Estimates of Monotone and Convex Approximation of Smooth Functions. J. of Approximation Theory 80, 1 (1995): 76-107. (.pdf)

·       Pointwise and Uniform Estimates for Convex Approximation of Functions by Algebraic Polynomials. Constructive Approximation 10, 2 (1994): 153-178. (.pdf)

·       On Some Permanental Conjectures. Linear and Multilinear Algebra 36 (1994): 205-216.  (.pdf)

·       (with V. V. Listopad) Remarks on Monotone and Convex Approximation by Algebraic Polynomials. Ukr. Mat. Zh. 46, 9 (1994): 1266-1270; Ukrainian Mathematical J. 46, 9 (1994): 1393-1398. (.pdf)

·       Uniform Estimates of Convex Approximation of Functions by Polynomials. Mat. Zametki 51, 3 (1992): 35-46. (.pdf) English translation: Mathematical Notes 51, 3 (1992): 245-254.  (.pdf)

·       Book edited: Trends in Approximation Theory (edited with T. Lyche and M. Neamtu), Vanderbilt Univ. Press, Nashville, TN, 2001, 512 pages.