The articles in this collection present new results in analysis, combinatorics, probability, theory of functions, and partial differential equations. The material presented in the book will be of interest to a broad range of specialists.

In several papers, the authors study the classical solvability of the Cauchy-Dirichlet problem for a class of parabolic systems, the solvability of the Dirichlet problem for the quasilinear second order parabolic systems, estimates for solutions of uniformly elliptic systems, and generalizations of the embedding theorems. In other papers, the authors describe a new method for the computation of correlation dimension, present generalizations of the fast Fourier transform method for wavelet expansions, and study the spectrum of two-dimensional periodic magnetic Schrödinger operator.

Readership

Graduate students and research mathematicians interested in analysis, combinatorics, probability, theory of functions, or partial differential equations.

Table of Contents

• A. A. Arkhipova -- On classical solvability of the Cauchy-Dirichlet problem for nondiagonal parabolic systems in the case of two spatial variables
• A. D. Baranov -- The Bernstein inequality in the de Branges spaces and embedding theorems
• V. O. Kal'vin -- The oblique derivative problem in spaces with asymptotics on edges
• V. N. Malozemov and S. M. Masharsky -- Glassman's formula, fast Fourier transform, and wavelet expansions
• A. I. Nazarov -- Dirichlet problem for quasilinear parabolic equations in domains with smooth closed edges
• S. I. Repin -- Two-sided estimates of deviation from exact solutions of uniformly elliptic equations
• J. V. Romanovsky and L. A. Evdokimov -- Calculation of correlation dimension of a time series based on enumeration of suboptimal solutions
• N. A. Shirokov -- Approximation by entire functions of an infinite system of closed intervals
• R. G. Shterenberg -- Absolute continuity of the spectrum of the two-dimensional magnetic periodic Schrödinger operator with positive electric potential