|Table of Contents|

Direct Theorems of Rational Approximation on Quasidisk(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1997年04期
Page:
98-100
Research Field:
Publishing date:

Info

Title:
Direct Theorems of Rational Approximation on Quasidisk
Author(s):
Wang Chaofu Wei Zhihui
School of Sciences, NUST, Nanjing 210094
Keywords:
elementary functions analyt ic funct io ns appr oximat ions quasidisk
PACS:
O350.1
DOI:
-
Abstract:
In this paper , it is given that tw o direct theorems using rat io nal functions to approx imate analyt ic funct io ns on quasidisks i. e. , assume that %be a close k-quasidisk, 0 ≤k ≤1, and f ( z ) be analyt ic in %and continuous on %, then, %n, r 0 ( f ) = O( n - A ) , A= 1- k , w here %n, r o ( f ) = inf { úR- f ú%÷R∈Rg n, r 0 } . If w e fur ther assume f ( z ) ∈LipB, then w e have %N 0 n ( f ) = O( n - A ) , A= B( 1- k) . Where %n 0 n ( f ) = { úp ( z ) / Π N 0 j = 1 ( z - z j ) - f ú%÷p ( z ) ∈Pn ( z ) } and z 1, ?, z N 0 are out side %such that , for z ∈ %, 1 ≤ ûΠ N 0 j= 1 ( z - z j ) û ≤M.

References:

1 Ander son M J, Gehring W F, Hinkkanen A. Polynomial appr ox imat ion in quasidisks. Different ial Geometr y and Complex Analysis, 1985( 3) : 75~86
2 王朝甫. 拟圆肋上的有理逼近. 长沙: 湖南大学学报( 数学专辑) , 1988( 1) : 274~279
3 Gaier Diet er. 复变函数逼近论. 沈立中译. 长沙: 湖南教育出版社, 1985
4 Pommer enke Chr . Univalent Funct ions. Gobt ting er : Vandenho eck and Ruprent, 1975
5 Belyi I V. Conformal mapping s a nd the appro x imation of analytic funct ions in domains with a quasiconfomal boundar y . Mat h U SSR Sbo r nik, 1977, 31: 289~317

Memo

Memo:
-
Last Update: 2013-03-29