Spaces of sequences, sampling theorem, and functions of exponential type

Rodolfo Torres

Studia Mathematica (1991)

  • Volume: 100, Issue: 1, page 51-74
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Torres, Rodolfo. "Spaces of sequences, sampling theorem, and functions of exponential type." Studia Mathematica 100.1 (1991): 51-74. <http://eudml.org/doc/215873>.

@article{Torres1991,
abstract = {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.},
author = {Torres, Rodolfo},
journal = {Studia Mathematica},
keywords = {Fourier transform; compact support; spaces of distributions; periodic distributions; sampling theorem; Besov spaces},
language = {eng},
number = {1},
pages = {51-74},
title = {Spaces of sequences, sampling theorem, and functions of exponential type},
url = {http://eudml.org/doc/215873},
volume = {100},
year = {1991},
}

TY - JOUR
AU - Torres, Rodolfo
TI - Spaces of sequences, sampling theorem, and functions of exponential type
JO - Studia Mathematica
PY - 1991
VL - 100
IS - 1
SP - 51
EP - 74
AB - 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.
LA - eng
KW - Fourier transform; compact support; spaces of distributions; periodic distributions; sampling theorem; Besov spaces
UR - http://eudml.org/doc/215873
ER -

References

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