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Landau's necessary density conditions for LCA groups |
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| Authors: | Karlheinz Gröchenig Gitta Kutyniok Kristian Seip |
| Institution: | a Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria b Department of Statistics, Stanford University, Stanford, CA 94305, USA c Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway |
| Abstract: | We derive necessary conditions for sampling and interpolation of bandlimited functions on a locally compact abelian group in line with the classical results of H. Landau for bandlimited functions on Rd. Our conditions are phrased as comparison principles involving a certain canonical lattice. |
| Keywords: | Beurling density Sampling Interpolation Homogeneous approximation property Locally compact abelian group |
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