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 φ-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.
@article{bwmeta1.element.bwnjournal-article-smv100i1p51bwm,
author = {Rodolfo Torres},
title = {Spaces of sequences, sampling theorem, and functions of exponential type},
journal = {Studia Mathematica},
volume = {100},
year = {1991},
pages = {51-74},
zbl = {0751.46012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv100i1p51bwm}
}
Torres, Rodolfo. Spaces of sequences, sampling theorem, and functions of exponential type. Studia Mathematica, Tome 100 (1991) pp. 51-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv100i1p51bwm/
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