Абстракция - мать порядка? (Историко-методологические рассуждения о связи экономической науки и экономической политики)
The article deals with the relation between assumptions of economic theories and their politicval implications. Two canons of economic science are analyzed according to the degree of abstraction. A hypothesis is that the more abstract formal canon is connected with a liberal kind of economic policy whereas the more concrete canon presupposes an active state involvement in economic affairs. Several attempts at integrating both canons are studied separately (Marshall, Schumpeter, Eucken). Historic evidence is more or less consistent with the hypothesis stated above, but there happens to be one important exclusion: the general equilibrium theory is so abstract that it can imply opposite policies.
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 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.
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.