Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Basic result: let {zn} be a sequence of points of the unit disc and {kn} be a sequence of natural numbers, satisfying the conditions:[Figure not available: see fulltext.] Then for any bounded sequence of complex numbers[Figure not available: see fulltext.] there exists a sequence[Figure not available: see fulltext.] such that the function[Figure not available: see fulltext.] interpolates ω: where BΛ is the Blaschke product with zeros at the points λn(k)}, M is a constant,[Figure not available: see fulltext.]. if N=1 this theorem is proved by Earl (RZhMat, 1972, 1B 163). The idea of the proof, as in Earl, is that if the zeros {λn(k)} run through neighborhoods of the points zn, then the Blaschke products with these zeros interpolate sequences ω, filling some neighborhood of zero in the space Z∞. The theorem formulated is used to get interpolation theorems in classes narrower than H∞.
Язык оригинала | английский |
---|---|
Страницы (с-по) | 2139-2143 |
Число страниц | 5 |
Журнал | Journal of Soviet Mathematics |
Том | 34 |
Номер выпуска | 6 |
DOI | |
Состояние | Опубликовано - сен 1986 |
ID: 75954037