TY - JOUR

T1 - A converse approximation theorem on subsets of elliptic curves

AU - Khaustov, A. V.

AU - Shirokov, N. A.

PY - 2006/3

Y1 - 2006/3

N2 - Functions defined on closed subsets of elliptic curves equation presented are considered. The following converse theorem of approximation is established. Consider a function f : G → C. Assume that there is a sequence of polynomials Pn(ζ, w) in two variables, deg Pn ≤ n, such that the following inequalities are valid: equation presented where 0 < α < 1. Then the function f necessarily belongs to the class H α(G). The direct approximation theorem was proved in the previous paper by the authors. Thus, a constructive description of the class Hα(G) is obtained. Bibliography: 6 titles.

AB - Functions defined on closed subsets of elliptic curves equation presented are considered. The following converse theorem of approximation is established. Consider a function f : G → C. Assume that there is a sequence of polynomials Pn(ζ, w) in two variables, deg Pn ≤ n, such that the following inequalities are valid: equation presented where 0 < α < 1. Then the function f necessarily belongs to the class H α(G). The direct approximation theorem was proved in the previous paper by the authors. Thus, a constructive description of the class Hα(G) is obtained. Bibliography: 6 titles.

UR - http://www.scopus.com/inward/record.url?scp=31944448600&partnerID=8YFLogxK

U2 - 10.1007/s10958-006-0087-9

DO - 10.1007/s10958-006-0087-9

M3 - Article

AN - SCOPUS:31944448600

VL - 133

SP - 1756

EP - 1764

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -