Constructive Description of Hölder Classes on Some Multidimensional Compact Sets

Vestnik St. Petersburg University, Mathematics - Tập 54 Số 3 - Trang 245-253 - 2021
Д. А. Павлов1
1Herzen State Pedagogical University of Russia, St. Petersburg, Russia

Tóm tắt

Từ khóa


Tài liệu tham khảo

V. K. Dzyadyk, “Constructive characterization of functions satisfying the condition Lip α(0 < α < 1) on a finite segment of the real axis,” Izv. Akad. Nauk SSSR, Ser. Mat. 20, 623–642 (1956).

V. V. Andrievskiĭ, “The geometric structure of regions, and direct theorems of the constructive theory of functions,” Math. USSR-Sb. 54, 39–56 (1986). https://doi.org/10.1070/SM1986v054n01ABEH002959

N. A. Shirokov, “Approximation entropy of continua,” Dokl. Akad. Nauk SSSR 235, 546–549 (1977).

N. A. Shirokov, “Constructive descriptions of functional classes by polynomial approximations. I,” J. Math. Sci. 105, 2269–2291 (2001). https://doi.org/10.1023/A:1011393428151

T. A. Alexeeva and N. A. Shirokov, “Constructive description of Hölder-like classes on an arc in R3 by means of harmonic functions,” J. Approximation Theory 249, 105308 (2020). https://doi.org/10.1016/j.jat.2019.105308

D. A. Pavlov, “Constructive description of Hölder classes on compact subsets of R3,” Zap. Nauchn. Semin. POMI 491, 119–144 (2020).

E. M. Dyn’kin, “The pseudoanalytic extension,” J. Anal. Math. 60, 45–70 (1993). https://doi.org/10.1007/BF03341966

S. G. Mikhlin, A Course of Mathematical Physics (Nauka, Moscow, 1968) [in Russian].