Book
Теория активных систем (ТАС-2014) [Электронный ресурс]: Материалы международной научно-практической конференции, 17–19 нояб. 2014 г, Москва
![Теория активных систем (ТАС-2014) [Электронный ресурс]: Материалы международной научно-практической конференции, 17–19 нояб. 2014 г, Москва](/f/src/pubs/default.png)
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on 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.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.