Causality and local analyticity : mathematical study
Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc
The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.
Der Zusammenhang zwischen der Randwertaufgabe von Riemann und einem Problem der mathematischen Musiktheorie
Difference equations for functions analytic beyond several squares.
Factorization of rational matrix functions and difference equations
In the beginning of the twentieth century, Plemelj introduced the notion of factorization of matrix functions. The matrix factorization finds applications in many fields such as in the diffraction theory, in the theory of differential equations and in the theory of singular integral operators. However, the explicit formulas for the factors of the factorization are known only in a few classes of matrices. In the present paper we consider a new approach to obtain the factorization of a rational matrix...
Funktionalgleichungen und Randwertaufgaben
Global geometric aspects of Riemann-Hilbert problems.
Holomorphic motions commuting with semigroups
A holomorphic family , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions which, in addition, commute with some holomorphic families of holomorphic endomorphisms of , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.
Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices.
Inversion of the Cauchy integral taken over the double periodic line.
Long time asymptotics of the Camassa–Holm equation on the half-line
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation on the half-line . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane , having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data...
Meromorphic extendibility and the argument principle.
Multiplicity of positive solutions for second order quasilinear equations
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
Nonlinear transmission problems.
On a necessary condition for interpolation by functions in the Lipschitz class.
On a problem of linear conjugation in the case of nonsmooth lines and some measurable coefficients.
On a representation of the derivative of a conformal mapping.
On boundary behavior of Cauchy integrals
In this paper, we shall estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain. By using the estimate, we shall generalize Plemelj-Sokthoski theorem. We also consider the boundary behavior of generalized Cauchy integrals on compact bordered Riemann surfaces.
On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical
We consider a certain analog of Cauchy type integral taking values in a three-dimensional harmonic algebra with two-dimensional radical. We establish sufficient conditions for an existence of limiting values of this integral on the curve of integration.
On meromorphic equivalence of linear difference operators
We consider linear difference equations whose coefficients are meromorphic at . We characterize the meromorphic equivalence classes of such equations by means of a system of meromorphic invariants. Using an approach inspired by the work of G. D. Birkhoff we show that this system is free.