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Zero sets and interpolating sets in Fock spaces
Author(s):
James
Tung
Journal:
Proc. Amer. Math. Soc.
134
(2006),
259-263.
MSC (2000):
Primary 30E05;
Secondary 46E15
Posted:
June 14, 2005
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Abstract:
An example is constructed to show that interpolating sets for Fock spaces are not necessarily zero sets.
References:
-
- 1.
- R. P. Boas, Entire Functions, Academic Press, New York, NY, 1954. MR 0068627 (16:914f)
- 2.
- C. Horowitz, Zeros of functions in the Bergman spaces, Duke Math. J. 41 (1974), 693-710. MR 0357747 (50:10215)
- 3.
- P. Duren and A. Schuster, Bergman Spaces, American Mathematical Society, Providence, RI, 2004. MR 2033762
- 4.
- K. Seip, Density theorems for sampling and interpolation in the Bargmann-Fock space I, J. Reine. Angew. Math. 429 (1992), 91-106. MR 1173117 (93g:46026a)
- 5.
- K. Seip and R. Wallstén, Density theorems for sampling and interpolation in the Bargmann-Fock space II, J. Reine. Angew. Math. 429 (1992), 107-113. MR 1173118 (93g:46026b)
- 6.
- K. Zhu, Zeros of functions in Fock spaces, Complex Variables Theory Appl. 21 (1993), 87-98.MR 1276563 (95b:30037)
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Additional Information:
James
Tung
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104
Email:
ytung@umich.edu
DOI:
10.1090/S0002-9939-05-07988-8
PII:
S 0002-9939(05)07988-8
Keywords:
Entire functions,
interpolating sequences,
zero sets
Received by editor(s):
August 2, 2004
Received by editor(s) in revised form:
September 3, 2004
Posted:
June 14, 2005
Additional Notes:
This paper is part of the author's dissertation at the University of Michigan under the direction of Professor Peter Duren. The author also thanks Joaquim Ortega-Cerdà for helpful discussions.
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2005,
American Mathematical Society
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