×

Fourier series and the Colombeau algebra on the unit circle. (English) Zbl 1175.46034

Summary: We give a simple construction of the Colombeau algebra in the setting of \(2\pi\)-periodic functions. The canonical embedding is provided by the Fourier series expansion. We develop the basic theory and discuss several examples of products.

MSC:

46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
42A10 Trigonometric approximation
PDF BibTeX XML Cite
Full Text: EuDML