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arXiv · 1604.02860

Some extensions to the functional analytic approach to Colombeau algebra

Eduard A. Nigsch
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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.

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BibTeXRIS

Eduard A. Nigsch. 2016-04-11. Some extensions to the functional analytic approach to Colombeau algebra. https://arxiv.org/abs/1604.02860

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