English

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.

Keywords

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

R2 v1 2026-06-22T13:29:12.800Z