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Article

On the topological stability of continuous functions in certain spaces related to Fourier series

Izvestiya. Mathematics. 2010. Vol. 74. No. 2. P. 347-378.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators in these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.