Multiple interpolation by Blaschke products

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Multiple interpolation by Blaschke products. / Videnskii, I. V.

In: Journal of Soviet Mathematics, Vol. 34, No. 6, 09.1986, p. 2139-2143.

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Videnskii, I. V. / Multiple interpolation by Blaschke products. In: Journal of Soviet Mathematics. 1986 ; Vol. 34, No. 6. pp. 2139-2143.

BibTeX

@article{42bcbbe4d6e9488ebe14415beaa33884,

title = "Multiple interpolation by Blaschke products",

abstract = "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∞.",

author = "Videnskii, {I. V.}",

year = "1986",

month = sep,

doi = "10.1007/BF01741588",

language = "English",

volume = "34",

pages = "2139--2143",

journal = "Journal of Mathematical Sciences (Switzerland)",

issn = "1072-3374",

publisher = "Springer Nature",

number = "6",

}

RIS

TY - JOUR

T1 - Multiple interpolation by Blaschke products

AU - Videnskii, I. V.

PY - 1986/9

Y1 - 1986/9

N2 - 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∞.

AB - 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∞.

UR - http://www.scopus.com/inward/record.url?scp=34250128976&partnerID=8YFLogxK

U2 - 10.1007/BF01741588

DO - 10.1007/BF01741588

M3 - Article

AN - SCOPUS:34250128976

VL - 34

SP - 2139

EP - 2143

JO - Journal of Mathematical Sciences (Switzerland)

JF - Journal of Mathematical Sciences (Switzerland)

SN - 1072-3374

IS - 6

ER -

ID: 75954037