### 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 inequalities
between 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 $L_\infty$-norms
of 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 proof
of Markov inequality and some of its generalizations,

Approx. Theory and its Appl. 8 (1992), 51-61.
On the approximation of functions by interpolating splines
defined 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 interpolation
of 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 functions
by 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.