Математика и физика. Mathematics & Physics. 2019 12 (4)
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Domains of Convergence for A-hypergeometric Series and Integrals
(Сибирский федеральный университет. Siberian Federal University, 2019-08)We prove two theorems on the domains of convergence for A-hypergeometric series and for associated Mellin-Barnes type integrals. The exact convergence domains are described in terms of amoebas and coamoebas of the ... -
The Closure and the Interior of C-convex Sets
(Сибирский федеральный университет. Siberian Federal University, 2019-08)C-convexity of the closure, interiors and their lineal convexity are considered for C-convex sets under additional conditions of boundedness and nonempty interiors. The following questions on closure and the interior of ... -
Locally Explicit Fundamental Principle for Homogeneous Convolution Equations
(Сибирский федеральный университет. Siberian Federal University, 2019-08)In the present paper a locally explicit version of Ehrenpreis’s Fundamental Principle for a system of homogeneous convolution equations f μ j = 0, j = 1; : : : ;m, f ∈ E(Rⁿ), μ j ∈ E′(Rⁿ), is derived, when the Fourier ... -
On Integration of Functions of Complexity One
(Сибирский федеральный университет. Siberian Federal University, 2019-08)We describe functions of complexity one with antiderivative of the same complexity -
The Discrete Analog of the Newton-Leibniz Formula in the Problem of Summation over Simplex Lattice Points
(Сибирский федеральный университет. Siberian Federal University, 2019-08)Definition of the discrete primitive function is introduced in the problem of summation over simplex lattice points. The discrete analog of the Newton-Leibniz formula is found -
The de Rham Cohomology through Hilbert Space Methods
(Сибирский федеральный университет. Siberian Federal University, 2019-08)We discuss canonical representations of the de Rham cohomology on a compact manifold with boundary. They are obtained by minimising the energy integral in a Hilbert space of differential forms that belong along with the ... -
Adiabatic Limit in Yang–Mills Equations in R⁴
(Сибирский федеральный университет. Siberian Federal University, 2019-08)Our goal is to present an approach to the proof of the harmonic spheres conjecture based on the adiabatic limit construction. This construction allows to associate with an arbitrary Yang–Mills G-field on the Euclidean ... -
Fine-analytic Functions in C ⁿ
(Сибирский федеральный университет. Siberian Federal University, 2019-08)In this paper we study class of fine-analytic functions in the multidimensional space C ⁿ: The definition of fine-analytic functions in the multidimensional case differs somewhat from the well-known definition of ... -
Functions with the One-dimensional Holomorphic Extension Property
(Сибирский федеральный университет. Siberian Federal University, 2019-08)In this paper we consider different families of complex lines, sufficient for holomorphic extension the functions f, defined on the boundary of a domain D Cn, n > 1, into this domain, and possessing the one-dimensional ... -
On Some Approach for Finding the Resultant of Two Entire Functions
(Сибирский федеральный университет. Siberian Federal University, 2019-08)One approach for finding the resultant of two entire functions is discussed in the article. It is based on Newton’s recurrent formulas -
On Carleman-type Formulas for Solutions to the Heat Equation
(Сибирский федеральный университет. Siberian Federal University, 2019-08)We apply the method of integral representations to study the ill-posed Cauchy problem for the heat equa- tion. More precisely we recover a function, satisfying the heat equation in a cylindrical domain, via its values ... -
Unified Transform method for the Schr¨odinger Equation on a Simple Metric Graph
(Сибирский федеральный университет. Siberian Federal University, 2019-08)Integral-representation of solutions of the initial-boundary value problems for the Schr¨odinger equation on simple metric graphs was obtained with the use of the Fokas method. This method uses special gen- eralization ... -
Upper Half-plane in the Grassmanian Gr(n; 2n)
(Сибирский федеральный университет. Siberian Federal University, 2019-08)We investigate the complex geometry of a multidimensional generalization D(n) of the upper-half-plane, which is homogeneous relative the group G = SL(2n;R). For n > 1 it is the pseudo Hermitian symmet- ric space which ... -
A Priori Estimates of the Conjugate Problem Describing an Axisymmetric Thermocapillary Motion for Small Marangoni Number
(Сибирский федеральный университет. Siberian Federal University, 2019-08)This paper is devoted to the study of equations solution describing the axisymmetric motion of a viscous heat-conducting liquid. The motion is interpreted as a two-layer flow of viscous heat-conducting liquids in a ...