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.


46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
42A10 Trigonometric approximation
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