Generalized interpolation in a multiply connected region

Authors:
Hari Bercovici and Adele Zucchi

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2109-2113

MSC (1991):
Primary 47A45; Secondary 47B35, 30D55, 30E05

DOI:
https://doi.org/10.1090/S0002-9939-96-03286-8

MathSciNet review:
1322912

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we extend to the case of multiply connected regions the famous result of Sarason concerning the characterization of operators commuting with the compression of the unilateral shift on to a co-invariant subspace.

**1.**M. B. Abrahamse,*The Pick Interpolation Theorem for finitely connected domains,*Michigan Math. J.**26**(1979), 195-203. MR**80j:30052****2.**M. B. Abrahamse,*Toeplitz Operators in multiply connected regions,*Amer. J. Math.**96**(1974), 261-297. MR**50:14333****3.**M. B. Abrahamse and R. G. Douglas,*A Class of Subnormal Operators related to multiply connected domains,*Advances in Math.**19**(1976), 106-148. MR**53:1327****4.**J. A. Ball and K. F. Clancey,*Reproducing Kernels for Hardy Spaces on multiply connected domains,*Preprint.**5.**H. Bercovici,*Operator Theory and Arithmetic in ,*Amer. Math. Soc., Providence, Rhode Island (1988). MR**90e:47001****6.**S. Fisher,*Function Theory on Planar Domains, a second course in Complex Analysis,*Wiley, New York (1983). MR**85d:30001****7.**H. L. Royden,*Invariant subspaces of**for multiply connected regions,*Pacific J. Math.**134**(1988), 151-172. MR**90a:46056****8.**B. Sz.-Nagy and C. Foias,*Dilatations des commutants d'opérateurs,*C. R. Acad. Sci. Paris Ser. A**266**(1968), 493-495. MR**38:5049****9.**W. Rudin,*Analytic functions of class*, Trans. Amer. Math. Soc.**78**(1955), 46-66. MR**16:810b****10.**D. Sarason,*Generalized Interpolation in*, Trans. Amer. Math. Soc.**127**(1967), 179-203. MR**34:8193****11.**A. Zucchi, Ph.D. Dissertation, Indiana University, Bloomington (1994).

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Additional Information

**Hari Bercovici**

Affiliation:
Department of Mathematics, Indiana University, Rawles Hall, Bloomington, Indiana 47405-5701

Email:
bercovic@indiana.edu

**Adele Zucchi**

Affiliation:
Department of Mathematics, Indiana University, Rawles Hall, Bloomington, Indiana 47405-5701

DOI:
https://doi.org/10.1090/S0002-9939-96-03286-8

Received by editor(s):
November 28, 1994

Received by editor(s) in revised form:
January 27, 1995

Additional Notes:
The first author was supported in part by grants from the National Science Foundation

The second author was supported in part by the Istituto Nazionale di Alta Matematica “F. Severi" of Italy

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society