Summary
We consider two equivalent density concepts for the unit disk that provide a complete description of sampling and interpolation inA −n (the Banach space of functionsf analytic in the unit disk with (1-|z|2)n|f(z)| bounded). This study reveals a ‘Nyquist density’: A sequence of points is (roughly speaking) a set of sampling if and only if its density in every part of the disk is strictly larger thann, and it is a set of interpolation if and only if its density in every part of the disk is strictly smaller thann. Similar density theorems are also obtained for weighted Bergman spaces.
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Oblatum 9-I-1992 & 10-XII-1992
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Seip, K. Beurling type density theorems in the unit disk. Invent Math 113, 21–39 (1993). https://doi.org/10.1007/BF01244300
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DOI: https://doi.org/10.1007/BF01244300