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Constructive descriptions of functional classes by polynomial approximations. I. / Shirokov, N. A.

In: Journal of Mathematical Sciences , Vol. 105, No. 4, 341658, 2001, p. 2269-2291.

Research output: Contribution to journal › Article › peer-review

Harvard

Shirokov, NA 2001, 'Constructive descriptions of functional classes by polynomial approximations. I', Journal of Mathematical Sciences , vol. 105, no. 4, 341658, pp. 2269-2291. https://doi.org/10.1023/A:1011393428151

APA

Shirokov, N. A. (2001). Constructive descriptions of functional classes by polynomial approximations. I. Journal of Mathematical Sciences , 105(4), 2269-2291. [341658]. https://doi.org/10.1023/A:1011393428151

Vancouver

Shirokov NA. Constructive descriptions of functional classes by polynomial approximations. I. Journal of Mathematical Sciences . 2001;105(4):2269-2291. 341658. https://doi.org/10.1023/A:1011393428151

Author

Shirokov, N. A. / Constructive descriptions of functional classes by polynomial approximations. I. In: Journal of Mathematical Sciences . 2001 ; Vol. 105, No. 4. pp. 2269-2291.

BibTeX

@article{5a414e6abf6749e8898fcae6191a1c48,
title = "Constructive descriptions of functional classes by polynomial approximations. I",
abstract = "Proofs of results announced earlier are given. Theorem 1, which was announced in 1976, states that a function on a domain with bounded boundary rotation can be approximated in terms of a function p1*(z), which modifies the classical distance p 1/nα(z) for the points whose neighborhoods contain more than one arc of the level curve of the complement of the domain. Theorem 2, which was announced in 1977, provides a domain with bounded boundary rotation and a function in the analytic H{\"o}lder α-class on the domain which cannot be approximated with precision P1/nα(z) by polynomials.",
author = "Shirokov, {N. A.}",
year = "2001",
doi = "10.1023/A:1011393428151",
language = "English",
volume = "105",
pages = "2269--2291",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "4",

}

RIS

TY - JOUR

T1 - Constructive descriptions of functional classes by polynomial approximations. I

AU - Shirokov, N. A.

PY - 2001

Y1 - 2001

N2 - Proofs of results announced earlier are given. Theorem 1, which was announced in 1976, states that a function on a domain with bounded boundary rotation can be approximated in terms of a function p1*(z), which modifies the classical distance p 1/nα(z) for the points whose neighborhoods contain more than one arc of the level curve of the complement of the domain. Theorem 2, which was announced in 1977, provides a domain with bounded boundary rotation and a function in the analytic Hölder α-class on the domain which cannot be approximated with precision P1/nα(z) by polynomials.

AB - Proofs of results announced earlier are given. Theorem 1, which was announced in 1976, states that a function on a domain with bounded boundary rotation can be approximated in terms of a function p1*(z), which modifies the classical distance p 1/nα(z) for the points whose neighborhoods contain more than one arc of the level curve of the complement of the domain. Theorem 2, which was announced in 1977, provides a domain with bounded boundary rotation and a function in the analytic Hölder α-class on the domain which cannot be approximated with precision P1/nα(z) by polynomials.

UR - http://www.scopus.com/inward/record.url?scp=52549090018&partnerID=8YFLogxK

U2 - 10.1023/A:1011393428151

DO - 10.1023/A:1011393428151

M3 - Article

AN - SCOPUS:52549090018

VL - 105

SP - 2269

EP - 2291

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

M1 - 341658

ER -

ID: 86660858