Математические методы распознавания образов: 15-я Всероссийская конференция, г.Петрозаводск, 11–17 сентября 2011 г.: Сборник докладов
The volume contains the abstracts of the 12th International Conference "Intelligent Data Processing: Theory and Applications". The conference is organized by the Russian Academy of Sciences, the Federal Research Center "Informatics and Control" of the Russian Academy of Sciences and the Scientific and Coordination Center "Digital Methods of Data Mining". The conference has being held biennially since 1989. It is one of the most recognizable scientific forums on data mining, machine learning, pattern recognition, image analysis, signal processing, and discrete analysis. The Organizing Committee of IDP-2018 is grateful to Forecsys Co. and CFRS Co. for providing assistance in the conference preparation and execution. The conference is funded by RFBR, grant 18-07-20075. The conference website http://mmro.ru/en/.
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.