Abstract:
Exact values have been found, for the diameters in the sense of Kolmogorov of certain classes of functions with a Hardy metric, analytic in the unit circle, whose boundary values admit of a representation by a convolution or the averaged modulus of smoothness of their boundary values is majorized by a given function. In passing, certain extremal properties of trigonometric polynomials are established.
M. Sh. Shabozov, A. A. Shabozova, “O sovmestnom priblizhenii nekotorykh klassov funktsii v prostranstve Bergmana B2”, Izv. vuzov. Matem., 2024, no. 6, 80–88
M. Sh. Shabozov, A. A. Shabozova, “On Simultaneous Approximation of Certain Classes of Functions in the Bergman Space B2”, Russ Math., 68:6 (2024), 68
Mirgand Sh. Shabozov, Muqim S. Saidusajnov, “On widths of some classes of analytic functions in a circle”, Ural Math. J., 10:2 (2024), 121–130
M. Sh. Shabozov, A. A. Shabozova, “O tochnykh znacheniyakh poperechnikov klassov analiticheskikh v kruge funktsii”, Matem. tr., 27:4 (2024), 115–140
M. R. Langarshoev, “Nailuchshee priblizhenie i znacheniya poperechnikov
nekotorykh klassov analiticheskikh funktsii v vesovom prostranstve
Bergmana B2,γ”, Vestnik rossiiskikh universitetov. Matematika, 28:142 (2023), 182–192
M. Sh. Shabozov, “On the Best Simultaneous Approximation in the Bergman Space B2”, Math. Notes, 114:3 (2023), 377–386
M. Sh. Shabozov, “O nailuchshem sovmestnom priblizhenii funktsii v prostranstve Khardi”, Tr. IMM UrO RAN, 29, no. 4, 2023, 283–291
M. Sh. Shabozov, Z. Sh. Malakbozov, “Sharp Jackson–Stechkin type inequalities in Hardy space H2 and widths of functional classes”, Ufa Math. J., 15:2 (2023), 74–84
M. Sh. Shabozov, G. A. Yusupov, “O nailuchshem polinomialnom priblizhenii funktsii v prostranstve Khardi Hq,R,(1⩽q⩽∞,R⩾1)”, Chebyshevskii sb., 24:1 (2023), 182–193
M. Sh. Shabozov, Z. Sh. Malakbozov, “On the best polynomial approximation in Hardy space”, Russian Math. (Iz. VUZ), 66:11 (2022), 97–109
M. Sh. Shabozov, G. A. Yusupov, D. D. Zargarov, “O nailuchshei sovmestnoi polinomialnoi approksimatsii funktsii i ikh proizvodnykh v prostranstve Khardi”, Tr. IMM UrO RAN, 27, no. 4, 2021, 239–254
S. B. Vakarchuk, “Estimates of the Values of n-Widths of Classes of Analytic Functions in the Weight Spaces H2,γ(D)”, Math. Notes, 108:6 (2020), 775–790
M. R. Langarshoev, “O nailuchshem polinomialnom priblizhenii funktsii v vesovom prostranstve Bergmana”, Vladikavk. matem. zhurn., 21:1 (2019), 27–36
M. Sh. Shabozov, M. R. Langarshoev, “Best linear approximation methods for some classes of analytic functions on the unit disk”, Siberian Math. J., 60:6 (2019), 1101–1108
S.B. Vakarchuk, V.I. Zabutna, M.B. Vakarchuk, “The best polynomial approximations of some classes of analytic functions in the Hardy spaces”, Vìsn. Dnìpro unìv., Ser. Mat., 26:1 (2018), 8
M. S. Saidusainov, “O nailuchshikh lineinykh metodakh priblizheniya nekotorykh klassov analiticheskikh funktsii v vesovom prostranstve Bergmana”, Chebyshevskii sb., 17:1 (2016), 240–253
M. Sh. Shabozov, G. A. Yusupov, “Best approximation methods and widths for some classes of functions in Hq,ρ, 1⩽q⩽∞, 0<ρ⩽1”, Siberian Math. J., 57:2 (2016), 369–376
Langarshoev M.R., “On the Best Linear Methods of Approximation and the Exact Values of Widths for Some Classes of Analytic Functions in the Weighted Bergman Space”, Ukr. Math. J., 67:10 (2016), 1537–1551
Vakarchuk S.B., Vakarchuk M.B., “Inequalities of Kolmogorov Type for Analytic Functions of One and Two Complex Variables and their Applications to Approximation Theory”, Ukr. Math. J., 63:12 (2012), 1795–1819