Модели и методы тропической математики в прикладных задачах экономики и управления
The evaluation and analysis of effectiveness of social and social and political projects is one of the important components of the management system of such projects. Presently, no convincing methods for the evaluation of the social effectiveness of investment projects have been elaborated, both in theory and in practice. In the article the methods, which might supplement the traditional approaches to the evaluation of the effectiveness of social projects, are proposed.
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.