Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Finite unions of interpolation sequences


Authors: Peter Duren and Alexander P. Schuster
Journal: Proc. Amer. Math. Soc. 130 (2002), 2609-2615
MSC (2000): Primary 30H05, 46E15
DOI: https://doi.org/10.1090/S0002-9939-02-06356-6
Published electronically: February 4, 2002
MathSciNet review: 1900868
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A unified and relatively simple proof is given for some well-known results involving finite unions of uniformly separated sequences.


References [Enhancements On Off] (What's this?)

  • 1. L. Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921-930. MR 22:8129
  • 2. L. Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. 76 (1962), 547-559. MR 25:5186
  • 3. P. L. Duren, Theory of $H^{p}$ Spaces, Academic Press, New York, 1970; reprinted with supplement by Dover Publications, New York, 2000. MR 42:3552
  • 4. P. Duren, D. Khavinson, and H. S. Shapiro, Extremal functions in invariant subspaces of Bergman spaces, Illinois J. Math. 40 (1996), 202-210. MR 97h:30069
  • 5. J. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. MR 83g:30037
  • 6. C. Horowitz, Zeros of functions in the Bergman spaces, Duke Math. J. 41 (1974), 693-710. MR 50:10215
  • 7. C. Horowitz, Factorization theorems for functions in the Bergman spaces, Duke Math. J. 44 (1977), 201-213. MR 55:681
  • 8. V. Kabaila, Interpolation sequences for the $H_{p}$ classes in the case $p < 1$, Litovsk. Mat. Sb. 3 (1963), no. 1, 141-147 (in Russian). MR 32:217
  • 9. D. Luecking, Inequalities in Bergman spaces, Illinois J. Math. 25 (1981), 1-11. MR 82e:30072
  • 10. G. McDonald and C. Sundberg, Toeplitz operators on the disc, Indiana Univ. Math. J. 28 (1979), 595-611. MR 80h:47034
  • 11. C. W. Neville, A short proof of an inequality of Carleson's, Proc. Amer. Math. Soc. 65 (1977), 131-132. MR 56:3303
  • 12. H. S. Shapiro, Comparative approximation in two topologies, in Approximation Theory (Banach Center Publications, Vol. 4, PWN-Polish Scientific Publishers, Warsaw 1979), pp. 225-232. MR 80j:41064
  • 13. H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513-532. MR 24:A3280

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30H05, 46E15

Retrieve articles in all journals with MSC (2000): 30H05, 46E15


Additional Information

Peter Duren
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: duren@umich.edu

Alexander P. Schuster
Affiliation: Department of Mathematics, San Francisco State University, San Francisco, California 94131
Email: schuster@sfsu.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06356-6
Received by editor(s): August 14, 2000
Received by editor(s) in revised form: March 26, 2001
Published electronically: February 4, 2002
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society