Weighted- interpolation on non-uniformly separated sequences
Author:
Stanislav Ostrovsky
Journal:
Proc. Amer. Math. Soc. 138 (2010), 4413-4422
MSC (2000):
Primary 30H05, 30D15, 32A36
DOI:
https://doi.org/10.1090/S0002-9939-2010-10193-4
Published electronically:
June 15, 2010
MathSciNet review:
2680065
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We define a weighted--norm associated to a discrete sequence
in
and a weight function
. We then give a sufficient condition which ensures that we can always extend weighted-
data to global holomorphic functions which are also weighted-
. The condition is such that the so-called upper density of
is strictly less than one.
- 1. Berndtsson, B.; Ortega-Cerdà, J., On interpolation and sampling in Hilbert spaces of analytic functions. J. Reine Angew. Math. 464 (1995), 109-128. MR 1340337 (96g:30070)
- 2. Duren, P.; Schuster, A., Bergman spaces. Mathematical Surveys and Monographs, Vol. 100, American Mathematical Society, Providence, RI, 2004. MR 2033762 (2005c:30053)
- 3. Hörmander, L., An introduction to complex analysis in several variables. North-Holland, 1990. MR 1045639 (91a:32001)
- 4.
Lindholm, N., Sampling in weighted
spaces of entire functions in
and estimates of the Bergman kernel. J. Funct. Anal. 182 (2001), no. 2, 390-426. MR 1828799 (2002g:32007)
- 5.
Ortega-Cerdà, J.; Seip, K., Beurling-type density theorems for weighted
spaces of entire functions. J. Anal. Math. 75 (1998), 247-266. MR 1655834 (2000k:46030)
- 6. Ortega-Cerdà , J.; Schuster, A.; Varolin, D., Interpolation and sampling hypersurfaces for the Bargmann-Fock space in higher dimensions. Math. Ann. 335 (2006), no. 1, 79-107. MR 2217685 (2007d:32002)
- 7. Seip, K., Density theorems for sampling and interpolation in the Bargmann-Fock space. I. J. Reine Angew. Math. 429 (1992), 91-106. MR 1173117 (93g:46026a)
- 8. Seip, K., Beurling type density theorems in the unit disk. Invent. Math. 113 (1993), no. 1, 21-39. MR 1223222 (94g:30033)
- 9. Seip, K.; Wallstén, R. Density theorems for sampling and interpolation in the Bargmann-Fock space. II. J. Reine Angew. Math. 429 (1992), 107-113. MR 1173118 (93g:46026b)
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Additional Information
Stanislav Ostrovsky
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651
Email:
stas@math.sunsysb.edu
DOI:
https://doi.org/10.1090/S0002-9939-2010-10193-4
Keywords:
Interpolation,
$L^{2}$-methods,
Beurling density
Received by editor(s):
February 10, 2009
Published electronically:
June 15, 2010
Communicated by:
Mario Bonk
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.