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. |