Some extensions to the functional analytic approach to Colombeau algebra
Functional Analysis
2016-04-12 v1
Abstract
We extend the functional analytic approach to Colombeau-type spaces of nonlinear generalized functions in order to study algebras of tempered generalized functions. We obtain a definition of Fourier transform of nonlinear generalized functions which has a strict inversion theorem, agrees with the classical Fourier transform for tempered distributions and preserves well-known classical properties.
Cite
@article{arxiv.1604.02860,
title = {Some extensions to the functional analytic approach to Colombeau algebra},
author = {Eduard A. Nigsch},
journal= {arXiv preprint arXiv:1604.02860},
year = {2016}
}
Comments
11 pages