## Alexei Shadrin - List of Publications Landau--Kolmogorov inequality revisited in preparation (with G. Nikolov) On Markov--Duffin--Schaeffer inequalities with a majorant. II in preparation (with G. Nikolov) On Markov--Duffin--Schaeffer inequalities with a majorant. Volume in memory of B. Bojanov (pdf) (with S. Foucart, Yu. Kryakin) On the exact constant in the Jackson-Stechkin inequality
for the uniform metric, Constr. Approx. 29 (2009), no. 2, 157--179. (pdf) Twelve proofs of the Markov inequality, in: ''Approximation Theory: A volume dedicated to Borislav Bojanov'' (D. K. Dimitrov et al, Eds), Marin Drinov Acad. Publ. House, Sofia 2004, 233--299. (pdf) (with K. Kopotun) On $k$-monotone approximation by free knot splines, SIAM J. Math. Anal. 34 (2003), 901--924. (pdf) The $L_\infty$-norm of the $L_2$-spline projector is bounded
independently of the knot sequence. A proof of de Boor's conjecture, Acta Math. 187 (2001), 59-137. (pdf) On $L_p$-boundedness of the $L_2$-projector onto finite
element space manuscript, October 1998 (pdf) (with K. Scherer) New upper bound for the B-spline basis
condition number II.A proof of de Boor's $2^k$-conjecture, J. Approx. Theory 99 (1999), 217-229. (pdf) On $L_\infty$-boundedness of the $L_2$-projector onto splines with multiple notes, IGPM Preprint 157, April 1998. (pdf) On a problem of C. de Boor for multivariate $D^m$-splines,Trudy MI RAN 219 (1997), 420-452 (pdf) = Proc. Steklov Inst. Math. 219 (1997), 413-446. (pdf) A note on the least constant in Landau inequality on a
finite interval,in: ''Recent Progress in Inequalities'' (G.V.Mitrinovic, Ed.), Kluwer Acad. Publisher, 1998, 489-491. (pdf) (with D. Leviatan) On monotone and convex approximation
by splines with free knots Annals of Numerical Mathematics 4 (1997), 415-434. (pdf) (with K. Scherer) New upper bound for the B-spline basis
condition number, East J. Approx. 2 (1996), 331-342. (pdf) Error bounds for Lagrange interpolation,J. Approx. Theory 80 (1995), 25-49. On $L_p$-boundedness of the $L_2$-projector onto splines,J. Approx. Theory 77 (1994), 331-348. Interpolation by Lagrange polynomials. B-splines and bounds of
the error, Analysis Mathematica 20 (1994), 213-224. Letter to the editors apropos A. I. Zviagintsev's paper`An extremal problem for the norm of intermediate derivative', Matem. zametki 55 (1994), 154-156 = Math. Notes 55 (1994), 543-545. To the Landau-Kolmogorov problem on a finite interval,in: ''Open Problems in Approximation Theory'' (B. Bojanov, Ed.), SCT Publishing, Singapore, 1994, 192-204. Interpolation by Lagrange polynomials. Sharp constants in inequalitiesbetween the norms of derivatives on a finite inerval, Matem. zametki 54 (1993), 129-143
= Math. Notes 54 (1993), 1165-1173. Convergence of quintic splines in terms of a local mesh ratio,Bull. Novosibirsk Computing Center,
ser. Numerical Analysis, 1 (1993), 87-95. On sharp constants in inequalities between $L_\infty$-normsof derivatives on a finite interval, Dokl. AN 326 (1992), 50-53
= Russian Acad. Sci. Dokl. Math. 46 (1993), 231-235. Interpolation with Lagrange polynomials. A simple proofof Markov inequality and some of its generalizations, Approx. Theory and its Appl. 8 (1992), 51-61. On the approximation of functions by interpolating splinesdefined on non-uniform meshes, Matem. sbornik 181 (1990), 1236-1255
= Math. USSR Sbornik 71 (1992), 81-99. Inequalities of Kolmogorov type and estimates of spline
interpolationof periodic classes $W^m_2$, Matem. zametki 48 (1990), 132-139
= Math. Notes 48 (1990), 1058-1063. On the rate of convergence of interpolating splines
defined on non-uniform meshes,Dokl. AN SSSR 307 (1989), 1331-1334
= Soviet Math. Dokl. 40 (1990), 266-268. On error estimates for approximation of functions by
smoothing splines,in: ''Variational Difference Methods in Problems of
Numerical Analysis''(V.V.Smelov, Ed.), Computing Center, Novosibirsk, 1988, 147-162 (Russian). Precise estimates for uniform approximations of classes $W^2_2$by interpolating cubic splines, Soviet J. Numer. Anal. Math. Modelling
3 (1988), 325-335. Jackson's type theorems for monotone approximation of functionsby trigonometric polynomials, Matem. zametki 42 (1987), 790-809
= Math. Notes 42 (1987), 933-944. Orders of one-sided approximation of functions in $L_p$-metric,Anal. Math. 12 (1986), 175-184. Monotone approximation of functions by trigonometric polynomials, Matem. zametki 34 (1983), 375-386
= Math. Notes 34 (1983), 669-675. |