01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
30.05.1952
E-mail:
Keywords:
best polinomial approximation; best rational approximation; best spline approximation; direct theorem of approximation theory; inverse theorem of approximation theory; Bernstein type inequalities; Jackson type inequalities; Hardy space; Sobolev space; Smirnov space; Besov space; interpolation space.
Main publications:
Pekarskii A. A., “Neravestva tipa Bernshteina dlya proizvodnykh ratsionalnykh funktsii i obratnye teoremy ratsionalnoi approksimatsii”, Matem. sb., 124:4 (1984), 571–588
Pekarskii A. A., “Klassy analiticheskikh funktsii, opredelyaemye nailuchshimi ratsionalnymi priblizheniyami v $H_p$”, Matem. sb., 127:1 (1985), 3–20
Pekarskii A. A., “Chebyshevskie ratsionalnye priblizheniya v kruge, na okruzhnosti i na otrezke”, Matem. sb., 133:1 (1987), 86–102
Pekarskii A. A., “Ratsionalnye priblizheniya funktsii s proizvodnymi iz prostranstva V. I. Smirnova”, Algebra i analiz, 13:2 (2001), 165–190
T. S. Mardvilko, A. A. Pekarskii, “Application of the real Hardy-Sobolev space on the line to study the order of uniform rational approximations of functions”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2022), 16–36
2016
2.
T. S. Mardvilko, A. A. Pekarskii, “Conjugate Functions on the Closed Interval and Their Relationship with Uniform Rational and Piecewise Polynomial Approximations”, Mat. Zametki, 99:2 (2016), 248–261; Math. Notes, 99:2 (2016), 272–283
A. A. Pekarskii, “Conjugate functions and their connection with uniform rational and piecewise-polynomial approximations”, Mat. Sb., 206:2 (2015), 175–182; Sb. Math., 206:2 (2015), 333–340
A. A. Pekarskii, “Approximation to the Function $z^{\alpha}$ by Rational Fractions in a Domain with Zero External Angle”, Mat. Zametki, 91:5 (2012), 761–772; Math. Notes, 91:5 (2012), 714–724
T. S. Mardvilko, A. A. Pekarskii, “Direct and inverse theorems of rational approximation in the Bergman space”, Mat. Sb., 202:9 (2011), 77–96; Sb. Math., 202:9 (2011), 1327–1346
A. A. Pekarskii, “On the Elimination of Singularities of Meromorphic Functions with Finitely Many Poles $p^r$”, Mat. Zametki, 80:2 (2006), 317–319; Math. Notes, 80:2 (2006), 305–308
7.
A. A. Pekarskii, “Comparison of the Best Uniform Approximations of Analytic Functions in the Disk and on Its Boundary”, Trudy Mat. Inst. Steklova, 255 (2006), 227–232; Proc. Steklov Inst. Math., 255 (2006), 215–220
2004
8.
A. A. Pekarskii, “Bernstein type inequalities for arbitrary rational functions in the spaces $L_p$, $0<p<1$, on Lavrent'ev curves”, Algebra i Analiz, 16:3 (2004), 143–170; St. Petersburg Math. J., 16:3 (2005), 541–560
A. A. Pekarskii, “New Proof of the Semmes Inequality for the Derivative of the Rational Function”, Mat. Zametki, 72:2 (2002), 258–264; Math. Notes, 72:2 (2002), 230–236
A. A. Pekarskii, “Rational approximations of functions with derivative in a V. I. Smirnov space”, Algebra i Analiz, 13:2 (2001), 165–190; St. Petersburg Math. J., 13:2 (2002), 281–300
A. A. Pekarskii, “Norm comparison for rational functions in the Bloch space and the Carathéodory-Fejér space”, Algebra i Analiz, 11:4 (1999), 139–150; St. Petersburg Math. J., 11:4 (2000), 643–650
14.
A. A. Pekarskii, E. A. Rovba, “Uniform approximations of Stieltjes functions by means of an orthoprojection onto the set of rational functions”, Mat. Zametki, 65:3 (1999), 362–368; Math. Notes, 65:3 (1999), 302–307
A. A. Pekarskii, “Best uniform rational approximations of Markov functions”, Algebra i Analiz, 7:2 (1995), 121–132; St. Petersburg Math. J., 7:2 (1996), 277–285
A. A. Pekarskii, H. Stahl, “Bernstein type inequalities for derivatives of rational functions in $L_p$ spaces for $p<1$”, Mat. Sb., 186:1 (1995), 119–130; Sb. Math., 186:1 (1995), 121–131
A. A. Pekarskii, “Generalization of the Hardy–Littlewood theorem on functions with derivatives in the space $H_1$”, Mat. Zametki, 52:1 (1992), 87–93; Math. Notes, 52:1 (1992), 695–700
1990
19.
A. A. Pekarskii, “Estimate of the derivative of an algebraic polynomial”, Mat. Zametki, 47:3 (1990), 74–77; Math. Notes, 47:3 (1990), 275–277
1989
20.
A. A. Pekarskii, “Best rational approximation in the complex domain”, Trudy Mat. Inst. Steklov., 190 (1989), 222–233; Proc. Steklov Inst. Math., 190 (1992), 231–243
A. A. Pekarskii, “Direct and converse theorems of rational approximation in the spaces $L_p[-1,1]$ and $C[-1,1]$”, Dokl. Akad. Nauk SSSR, 293:6 (1987), 1307–1310
22.
A. A. Pekarskii, “Tchebycheff rational approximation in the disk, on the circle, and on a closed interval”, Mat. Sb. (N.S.), 133(175):1(5) (1987), 86–102; Math. USSR-Sb., 61:1 (1988), 87–102
A. A. Pekarskii, “Estimates of the derivatives of rational functions in $L_p[-1,1]$”, Mat. Zametki, 39:3 (1986), 388–394; Math. Notes, 39:3 (1986), 212–216
A. A. Pekarskii, “Classes of analytic functions determined by best rational approximations in $H_p$”, Mat. Sb. (N.S.), 127(169):1(5) (1985), 3–20; Math. USSR-Sb., 55:1 (1986), 1–18
A. A. Pekarskii, “Inequalities of Bernstein type for derivatives of rational functions, and inverse theorems of rational approximation”, Mat. Sb. (N.S.), 124(166):4(8) (1984), 571–588; Math. USSR-Sb., 52:2 (1985), 557–574
A. A. Pekarskii, “Estimates of the derivative of a Cauchy-type integral with meromorphic density and their applications”, Mat. Zametki, 31:3 (1982), 389–402; Math. Notes, 31:3 (1982), 199–206
A. A. Pekarskii, “Rational approximations of absolutely continuous functions with derivative in an Orlicz space”, Mat. Sb. (N.S.), 117(159):1 (1982), 114–130; Math. USSR-Sb., 45:1 (1983), 121–137
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