SPACES OF SEQUENCES, SAMPLING THEOREM, AND FUNCTIONS OF EXPONENTIAL TYPE

We introduce certain spaces of sequences which can be used to characterize spaces of functions of exponential type. We present a generalized version of the sampling theorem and a "nonorthogonal wavelet decomposition" for the elements of these spaces of sequences. In particular, we obtain a discrete version of the so-called phi-transform studied in [6]-[8]. We also show how these new spaces and the corresponding decompositions can be used to study multiplier operators on Besov spaces.