Sampling of Paley-Wiener functions on stratified groups
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We consider a generalization of entire functions of spherical exponential type on stratified groups. An analog of the Paley-Wiener theorem is given. We also show that every spectral entire function on a stratified group is uniquely determined by its values on some discrete subgroups. The main result of the article is reconstruction formula of spectral entire functions from their values on discrete subgroups using Lagrangian splines.
Math Subject ClassificationsPrimary 43A80 secondary 41A15, 41A17 Keywords and Phrases Stratified group sub-Laplacian Bernstein inequality Lagrangian spline
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