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- W2096119995 abstract "We give sufficient conditions for a closed smooth hypersurface W in the n-dimensional Bergman ball to be interpolating or sampling. As in the recent work [5] of Ortega-Cerdà, Schuster and the second author on the Bargmann–Fock space, our sufficient conditions are expressed in terms of a geometric density of the hypersurface that, though less natural, is shown to be equivalent to Bergman ball analogs of the Beurling-type densities used in [5]. In the interpolation theorem we interpolate L 2 data from W to the ball using the method of Ohsawa–Takegoshi, extended to the present setting, rather than the Cousin I approach used in [5]. In the sampling theorem, our proof is completely different from [5]. We adapt the more natural method of Berndtsson and Ortega-Cerdà [1] to higher dimensions. This adaptation motivated the notion of density that we introduced. The approaches of [5] and the present paper both work in either the case of the Bergman ball or of the Bargmann–Fock space." @default.
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- W2096119995 date "2007-05-01" @default.
- W2096119995 modified "2023-10-01" @default.
- W2096119995 title "SUFFICIENT CONDITIONS FOR INTERPOLATION AND SAMPLING HYPERSURFACES IN THE BERGMAN BALL" @default.
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- W2096119995 doi "https://doi.org/10.1142/s0129167x07004084" @default.
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