SAMPLING SEQUENCES OF COMPACTLY SUPPORTED DISTRIBUTIONS IN L{sub}P(R)

摘要

The aim of the paper is to obtain some generalizations of the so-called Plancherel-Polya inequalities which are also known as frame inequalities. By using these inequalities we show that a function f ∈ L{sub}p(R), 1 ≤ p ≤ ∞, which is entire function of exponential type is uniquely determined by a set of numbers {Φ{sub}j(f)}, j ∈ N where {Φ{sub}j}, j ∈ N is a countable sequence of compactly supported distributions. In the case p = 2 we offer two reconstruction methods of a function / from a sequence of samples {Φ{sub}j(f)}, j ∈ N. The first reconstruction algorithm is given in terms of frames. To describe our second algorithm we introduce the so-called average variational splines.