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.

**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.**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 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**

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