## 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
Full Text: