Advertisement

Journal of Soviet Mathematics

, Volume 34, Issue 6, pp 2139–2143 | Cite as

Multiple interpolation by Blaschke products

  • I. V. Videnskii
Article
  • 23 Downloads

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:
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.

Keywords

Natural Number Complex Number Unit Disc Basic Result Blaschke Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    L. Carleson, Ann. Math.,76, No. 3, 547–559 (1962).Google Scholar
  2. 2.
    J. P. Earl, J. London Math. Soc,2, No. 2, 544–548 (1970).Google Scholar
  3. 3.
    V. E. Katsnel'son, Punkts. Anal. Prim.,1, No. 2, 39–51 (1967).Google Scholar
  4. 4.
    V. I. Vasyunin, Dokl. Akad. Nauk SSSR,227, No. 1, 11–14 (1976).Google Scholar
  5. 5.
    N. K. Nikol'skii, Tr. Mat. Inst. Akad. Nauk SSSR,130, Nauka, Leningrad (1977).Google Scholar
  6. 6.
    P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory [in Russian], Moscow (1973).Google Scholar
  7. 7.
    S. A. Vinogradov and V. P. Khavin, J. Sov. Math.,9, No. 2 (1978).Google Scholar
  8. 8.
    S. A. Vinogradov and V. P. Khavin, J. Sov. Math.,14, No. 2 (1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • I. V. Videnskii

There are no affiliations available

Personalised recommendations