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Finite unions of interpolation sequences
Author(s):
Peter
Duren;
Alexander
P.
Schuster
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2609-2615.
MSC (2000):
Primary 30H05, 46E15
Posted:
February 4, 2002
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Abstract:
A unified and relatively simple proof is given for some well-known results involving finite unions of uniformly separated sequences.
References:
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- 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
 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.
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- 7.
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- 8.
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 classes in the case  , 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
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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:
10.1090/S0002-9939-02-06356-6
PII:
S 0002-9939(02)06356-6
Received by editor(s):
August 14, 2000
Received by editor(s) in revised form:
March 26, 2001
Posted:
February 4, 2002
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2002,
American Mathematical Society
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