Feichtinger, Hans G.;Pandey, S. S.;Werther, Tobias

Minimal norm interpolation in harmonic Hilbert spaces and Wiener amalgam spaces on locally compact abelian groups

J. Math. Kyoto Univ. Vol.47 No.1 (2007) p.65-78, Zbl:1138.43003, MR2359101


Harmonic Hilbert spaces are a natural enlargement of those classical L^2-Sobolev space on R^d which consist of continuous functions. In the present paper we demonstrate that the use of Wiener amalgam spaces allows to establish the basic properties of harmonic Hilbert spaces even if they are defined over an arbitrary locally compact abelian group G. For G = R^d this new approach improves previously known results. In the present paper we present in some detail results on minimal norm interpolators over lattices and show that the infinite minimal norm interpolations may be obtained as a limit of finite minimal norm interpolations. This paper paves the way for the study of stability problems and error analysis for norm interpolations in harmonic Hilbert and Banach spaces on locally compact abelian groups.
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