Multiple interpolation by Blaschke products

Autor:	I. V. Videnskii
Rok vydání:	1986
Předmět:	Statistics and Probability Discrete mathematics Sequence Applied Mathematics General Mathematics Blaschke product Zero (complex analysis) Natural number Function (mathematics) symbols.namesake Bounded function symbols Complex number Interpolation Mathematics
Zdroj:	Journal of Soviet Mathematics. 34:2139-2143
ISSN:	1573-8795 0090-4104
DOI:	10.1007/bf01741588
Popis:	Basic result: let {zn} be a sequence of points of the unit disc and {kn} be a sequence of natural numbers, satisfying the conditions: Then for any bounded sequence of complex numbers there exists a sequence such that the function interpolates ω: where BΛ is the Blaschke product with zeros at the points λn(k)}, M is a constant, . 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∞.
Databáze:	OpenAIRE
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