Статистические методы оценивания и проверки гипотез: межвузовский сборник научных трудов
In the paper we present a new notion of stochastic monotone measure and its application to image processing. By definition, a stochastic monotone measure is a random value with values in the set of monotone measures and it can describe a choice of random features in image processing. In this case, a monotone measure describes uncertainty in the problem of choosing the set of features with the highest value of informativeness and its stochastic behavior is explained by a noise that can corrupt images.
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.