# 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} }

. 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

### Explicit commutative sequence space representations of function and distribution spaces on the real half-line

- MathematicsArchiv der Mathematik
- 2022

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…

### Sequence Space Representations for Translation-Modulation Invariant Function and Distribution Spaces

- Materials ScienceJournal of Fourier Analysis and Applications
- 2022

We provide sequence space representations for the test function space DE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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