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Том 231, № 4 (2018)
- Год: 2018
- Статей: 8
- URL: https://journals.rcsi.science/1072-3374/issue/view/14922
Article
Development of the Theory of Branched Continued Fractions in 1996–2016
Аннотация
We perform the analysis of investigations in the theory of branched continued fractions carried out for the last 20 years in the directions developed under the general supervision of Prof. V. Ya. Skorobohat’ko (18.07.1927–04.07.1996) including, in particular, the interpolation of functions of several variables by branched continued fractions, the determination of efficient criteria of convergence and computational stability of these fractions, the correspondence between multiple power series and functional branched continued fractions, the investigation of various classes of functional fractions, and the application of branched continued fractions.
481-494
Integral Problem for a Partial Differential Equation of High Order in an Infinite Strip
Аннотация
We establish conditions for the existence, in the scale of Sobolev spaces, of a unique solution to the problem for partial differential equations of high order with integral conditions in the form of moments. The solution of this problem is constructed with the help of Fourier transforms.
495-506
On the Classical Fundamental Solutions of the Cauchy Problem for Ultraparabolic Kolmogorov-Type Equations with Two Groups of Spatial Variables
Аннотация
For a Kolmogorov-type ultraparabolic equation with two groups of spatial variables, we establish estimates for the increments of the classical fundamental solution of the Cauchy problem and its derivatives in the spatial variables.
507-526
527-535
Abstract Interpolating Fraction of the Thiele Type
Аннотация
We construct an abstract continued fraction of the Thiele type as an interpolating fraction for a nonlinear operator acting from a linear topological space X to an algebra Y with identity. In some special cases, this fraction transforms either into a classical Thiele fraction or into a matrix-valued fraction of the Thiele type depending on many variables.
536-546
Generalized Bessel–Struve Operator and Its Properties
Аннотация
We define the generalized Bessel–Struve operator in the space of functions analytic in an arbitrary domain. The conditions of equivalence of the generalized Bessel–Struve operator to the operator of second derivative are investigated. We also describe the commutant of the generalized Bessel–Struve operator and establish its hypercyclicity and chaotic nature.
547-557
A Nonlocal Inverse Problem for the Two-Dimensional Heat-Conduction Equation
Аннотация
We consider an inverse problem of determination of the time-dependent leading coefficient of a two-dimensional heat-conduction equation with nonlocal overdetermination condition. The existence and uniqueness conditions are established for the classical solution of the analyzed problem.
558-571
Nonlocal Boundary-Value Problem for a Differential-Operator Equation with Weak Nonlinearity in the Spaces of Dirichlet–Taylor Series with Fixed Spectrum
Аннотация
We study the nonlocal boundary-value problem for a differential-operator equation with nonlinear right-hand side and an operator B = (B1,…Bp), where its components Bj ≡ zj∂/∂zj, j = 1,…,p, are the operators of generalized differentiation with respect to the complex variable zj. By using the Nash–Moser iterative scheme, we establish the conditions of solvability of this problem in the scale of spaces of functions of several complex variables, which are Dirichlet–Taylor series with fixed spectrum.
572-585