Kirill Kopotun

Research and Teaching Interests

Approximation theory, computational and industrial mathematics, numerical analysis, linear algebra (matrix theory), partial differential equations

Education

• M.Sc. Kiev
• Ph.D. Alberta

Current graduate students

• Farzaneh Jannat (M.Sc. Thesis)
• Kyrylo Muliarchyk (M.Sc. Thesis)
• Sahar Rahimzad Lamey (M.Sc. Thesis)

Select publications

• Kopotun, K. A.; Leviatan, D. and Shevchuk, I. A. (2018). Interpolatory pointwise estimates for monotone polynomial approximation. J. Math. Anal. Appl. 459 (2), 1260–1295.
• Kopotun, K. A.; Leviatan, D.; Prymak, A. and Shevchuk, I. A. (2016). Yet another look at positive linear operators, q-monotonicity and applications. J. Approx. Theory 210, 1–22.
• Kopotun, Kirill A. (2016). Uniform polynomial approximation with A∗∗ weights having finitely many zeros. J. Math. Anal. Appl. 435 (1), 677–700.
• Kopotun, Kirill; Leviatan, Dany and Shevchuk, Igor (2016). Constrained approximation with Jacobi weights. Canad. J. Math. 68 (1), 109–128.
• Kopotun, K. A. (2015). Polynomial approximation with doubling weights. Acta Math. Hungar. 146 (2), 496–535.
• Kopotun, K. A.; Leviatan, D. and Shevchuk, I. A. (2015). New moduli of smoothness: weighted DT moduli revisited and applied. Constr. Approx. 42 (1), 129–159.
• Kopotun, Kirill A. (2015). Polynomial approximation with doubling weights having finitely many zeros and singularities. J. Approx. Theory 198, 24–62.
• Kopotun, Kirill A. (2015). Weighted moduli of smoothness of k-monotone functions and applications.J. Approx. Theory 192, 102–131.
• Kopotun, K. A.; Leviatan, D. and Shevchuk, I. A. (2014). New moduli of smoothness. Publ. Inst. Math. (Beograd) (N.S.) 96(110), 169–180.
• Kopotun, K. A.; Leviatan, D.; Prymak, A. and Shevchuk, I. A. (2011). Uniform and pointwise shape preserving approximation by algebraic polynomials. Surv. Approx. Theory 6, 24–74.
• Dzyubenko, G. A.; Kopotun, K. A. and Prymak, A. V. (2010). Three-monotone spline approximation. J. Approx. Theory 162 (12), 2168–2183.
• Konovalov, V. N.; Kopotun, K. A. and Maiorov, V. E. (2010). Convex polynomial and ridge approximation of Lipschitz functions in Rd. Rocky Mountain J. Math. 40 (3), 957–976.
• Kopotun, K.; Leviatan, D. and Shevchuk, I. A. (2010). Are the degrees of the best (co)convex and unconstrained polynomial approximations the same? II. Ukraı̈n. Mat. Zh. 62 (3), 369–386.
• Kopotun, Kirill A. and Popov, Bojan (2010). Moduli of smoothness of splines and applications in constrained approximation. Jaen J. Approx. 2 (1), 79–91.
• Kopotun, K. A.; Leviatan, D. and Prymak, A. V. (2009). Nearly monotone and nearly convex approximation by smooth splines in Lp, p>0. J. Approx. Theory 160 (1-2), 103–112.
• Kopotun, K.; Leviatan, D. and Shevchuk, I. A. (2009). Are the degrees of best (co)convex and unconstrained polynomial approximation the same?. Acta Math. Hungar. 123 (3), 273–290.
• Kopotun, Kirill (2009). On moduli of smoothness of k-monotone functions and applications. Math. Proc. Cambridge Philos. Soc. 146 (1), 213–223.
• Konovalov, Victor N. and Kopotun, Kirill A. (2008). Kolmogorov, linear and pseudo-dimensional widths of classes of s-monotone functions in Lp, 0<p<1. Canad. Math. Bull. 51 (2), 236–248.
• Kopotun, K.; Leviatan, D. and Prymak, A. V. (2008). Constrained spline smoothing. SIAM J. Numer. Anal. 46 (4), 1985–1997.
• Kopotun, Kirill A. (2007). Univariate splines: equivalence of moduli of smoothness and applications.Math. Comp. 76 (258), 931–945.
• Kopotun, K.; Leviatan, D. and Prymak, A. V. (2006). Nearly monotone spline approximation in Lp. Proc. Amer. Math. Soc. 134 (7), 2037–2047.
• Kopotun, K.; Leviatan, D. and Shevchuk, I. A. (2006). Coconvex approximation in the uniform norm: the final frontier. Acta Math. Hungar. 110 (1-2), 117–151.
• Kopotun, K.; Leviatan, D. and Shevchuk, I. A. (2006). Erratum to: “Coconvex approximation in the uniform norm: the final frontier” [Acta. Math. Hungar. bf 110 (2006), no. 1-2, 117–151; MR2198418].Acta Math. Hungar. 113 (3), 255.
• Kopotun, Kirill A. (2006). On equivalence of moduli of smoothness of splines in Lp, 0<p<1. J. Approx. Theory 143 (1), 36–43.
• Kopotun, K. A.; Leviatan, D. and Shevchuk, I. A. (2005). Convex polynomial approximation in the uniform norm: conclusion. Canad. J. Math. 57 (6), 1224–1248.
• Kopotun, Kirill A.. On k-monotone interpolation. In Advances in constructive approximation: Vanderbilt 2003 265–275. Nashboro Press, Brentwood, TN, 2004.
• Kopotun, Kirill; Neamtu, Marian and Popov, Bojan (2003). Weakly nonoscillatory schemes for scalar conservation laws. Math. Comp. 72 (244), 1747–1767.
• Kopotun, Kirill and Shadrin, Alexei (2003). On k-monotone approximation by free knot splines. SIAM J. Math. Anal. 34 (4), 901–924.
• Kopotun, K. A. (2001). Whitney theorem of interpolatory type for k-monotone functions. Constr. Approx. 17 (2), 307–317.
• Hu, Yingkang; Kopotun, Kirill A. and Yu, Xiang Ming (2000). Modified adaptive algorithms. SIAM J. Numer. Anal. 38 (3), 1013–1033.
• Hu, Y. K.; Kopotun, K. A. and Yu, X. M. (2000). On multivariate adaptive approximation. Constr. Approx. 16 (3), 449–474.
• Hu, Y. K.; Kopotun, K. A. and Yu, X. M. (1999). Weak copositive and intertwining approximation. J. Approx. Theory 96 (2), 213–236.
• Kopotun, K.; Leviatan, D. and Shevchuk, I. A. (1999). The degree of coconvex polynomial approximation. Proc. Amer. Math. Soc. 127 (2), 409–415.
• Kopotun, K. and Leviatan, D. (1998). Degree of simultaneous coconvex polynomial approximation.Results Math. 34 (1-2), 150–155. Dedicated to Paul Leo Butzer
• Kopotun, Kirill A. (1998). Approximation of k-monotone functions. J. Approx. Theory 94 (3), 481–493.
• Hu, Y. K.; Kopotun, K. A. and Yu, X. M. (1997). Constrained approximation in Sobolev spaces. Canad. J. Math. 49 (1), 74–99.
• Kopotun, K. and Leviatan, D. (1997). Comonotone polynomial approximation in Lp[−1,1], 0<p≤∞. Acta Math. Hungar. 77 (4), 301–310.
• Hu, Y. K.; Kopotun, K. A. and Yu, X. M. (1996). On positive and copositive polynomial and spline approximation in Lp[−1,1], 0<p<∞. J. Approx. Theory 86 (3), 320–334.
• Kopotun, K. (1996). Simultaneous approximation by algebraic polynomials. Constr. Approx. 12 (1), 67–94.
• Kopotun, Kirill A. (1996). A note on the convexity of the sum of subpermanents. Linear Algebra Appl. 245, 157–169.
• Kopotun, Kirill A. (1996). Shape preserving approximation. ProQuest LLC, Ann Arbor, MI.
• Kopotun, K. A. (1995). Unconstrained and convex polynomial approximation in C[−1,1]. Approx. Theory Appl. (N.S.) 11 (2), 41–58.
• Kopotun, Kirill (1995). A note on simultaneous approximation in Lp[−1,1] (1≤p<∞). Analysis 15 (2), 151–158.
• Kopotun, Kirill (1995). On copositive approximation by algebraic polynomials. Anal. Math. 21 (4), 269–283.
• Kopotun, Kirill A. (1995). Coconvex polynomial approximation of twice differentiable functions. J. Approx. Theory 83 (2), 141–156.
• Kopotun, Kirill A.. On K-monotone polynomial and spline approximation in Lp, 0<p<∞(quasi)norm. In Approximation theory VIII, Vol. 1 (College Station, TX, 1995) 295–302. World Sci. Publ., River Edge, NJ, 1995.
• Kopotun, Kirill A. (1995). Uniform estimates of monotone and convex approximation of smooth functions. J. Approx. Theory 80 (1), 76–107.
• Kopotun, K. A. and Listopad, V. V. (1994). Remarks on monotone and convex approximation by algebraic polynomials. Ukraı̈n. Mat. Zh. 46 (9), 1266–1270.
• Kopotun, Kirill A. (1994). On some permanental conjectures. Linear and Multilinear Algebra 36 (3), 205–216.
• Kopotun, Kirill A. (1994). Pointwise and uniform estimates for convex approximation of functions by algebraic polynomials. Constr. Approx. 10 (2), 153–178.
• Kopotun, K. A. (1992). Uniform estimates for coconvex approximation of functions by polynomials.Mat. Zametki 51 (3), 35–46, 143.

Courses taught

• MATH 4390 A01
• MATH 7390 A01

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