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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∞.
Original language | English |
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Pages (from-to) | 2139-2143 |
Number of pages | 5 |
Journal | Journal of Soviet Mathematics |
Volume | 34 |
Issue number | 6 |
DOIs | |
State | Published - Sep 1986 |
ID: 75954037