# Sequence space representations for spaces of smooth functions and distributions via Wilson bases

@inproceedings{Bargetz2021SequenceSR,
title={Sequence space representations for spaces of smooth functions and distributions via Wilson bases},
author={Christian Bargetz and Andreas Debrouwere and Eduard A. Nigsch},
year={2021}
}
• Published 1 July 2021
• Mathematics
. We provide explicit sequence space representations for the test function and distribution spaces occurring in the Valdivia-Vogt structure tables by making use of Wilson bases generated by compactly supported smooth windows. Furthermore, we show that these kind of bases are common unconditional Schauder bases for all separable spaces occurring in these tables. Our work implies that the Valdivia-Vogt structure tables for test functions and distributions may be interpreted as one large…
2 Citations
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Archiv der Mathematik
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We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the
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We provide sequence space representations for the test function space DE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}

## References

SHOWING 1-10 OF 24 REFERENCES

In this article, we show that the Valdivia–Vogt structure table—containing the sequence space representations of the most used spaces of smooth functions appearing in the theory of distributions—can
We prove precise decomposition results and logarithmically convex estimates in certain weighted spaces of holomorphic germs near R. These imply that the spaces have a basis and are tamely isomorphic
The traditional functional analysis deals mostly with Banach spaces and, in particular, Hilbert spaces. However, many classical vector spaces have canonical topologies that cannot be determined by a
• Mathematics
• 2004
We characterize several classes of test functions, among them Bjorck's ultra-rapidly decaying test functions and the Gelfand-Shilov spaces of type S, in terms of the decay of their short-time Fourier
WE give a representation of a class of infinitely differentiable complex functions defined on Rn. As consequence we obtain for n>1 that Open image in new window and Open image in new
Here we introduce the test-function space H∞(SR), which is the basic local element of the duality {H∞(G),H-∞(G)}.
In the Valdivia–Vogt structure tables presented in Ortner and Wagner (J Math Anal Appl 404(1):1–10, 2013) there are two gaps. We fill in these gaps by proving the representations \mathcal