О пространстве двоично-обобщенных функций
In this paper, we study scalar multivariate non-stationary subdivision
schemes with integer dilation matrix M and present a unifying, general approach
for checking their convergence and for determining their Hölder regularity (latter in
the case M = mI,m ≥ 2). The combination of the concepts of asymptotic similarity
and approximate sum rules allows us to link stationary and non-stationary settings
and to employ recent advances in methods for exact computation of the joint spectral
radius. As an application, we prove a recent conjecture by Dyn et al. on the Hölder regularity
of the generalized Daubechies wavelets. We illustrate our results with several
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.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.