On the Riemann-Hilbert problem with a piecewise constant matrix

Vladimir V. Mityushev; Sergei Rogosin

doi:10.4171/ZAA/1343

On the Riemann-Hilbert problem with a piecewise constant matrix

Vladimir V. Mityushev^*, Sergei Rogosin

^*Corresponding author for this work

Department of Physics

University of Pedagogical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

A constructive solution to the Riemann-Hilbert boundary value problem as well as to the C-linear conjugation problem (or Riemann problem) with a special piecewise constant matrix for a multiply connected domain is obtained. The result is based on a vector generalization of the scalar method of functional equations in complex domain and on application of the Christoffel-Schwarz transformation of the half-plane onto a circular polygon.

Original language	English
Pages (from-to)	53-66
Number of pages	14
Journal	Zeitschrift für Analysis und ihre Anwendungen
Volume	27
Issue number	1
DOIs	https://doi.org/10.4171/ZAA/1343
Publication status	Published - 2008

Keywords

functional equation
FACTORIZATION
multiply connected domain
vector-matrix C-linear conjugation problem
Riemann-Hilbert boundary value problem
Christoffel-Schwarz transformation

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title = "On the Riemann-Hilbert problem with a piecewise constant matrix",

abstract = "A constructive solution to the Riemann-Hilbert boundary value problem as well as to the C-linear conjugation problem (or Riemann problem) with a special piecewise constant matrix for a multiply connected domain is obtained. The result is based on a vector generalization of the scalar method of functional equations in complex domain and on application of the Christoffel-Schwarz transformation of the half-plane onto a circular polygon.",

keywords = "functional equation, FACTORIZATION, multiply connected domain, vector-matrix C-linear conjugation problem, Riemann-Hilbert boundary value problem, Christoffel-Schwarz transformation",

author = "Mityushev, \{Vladimir V.\} and Sergei Rogosin",

note = "Mityushev, V. V., Rogosin, S. V. (2008). On the Riemann-Hilbert problem with a piecewise constant matrix. Zeitschrift f{\"u}r Analysis und ihre Anwendungen, 27 (1), 53-66.",

year = "2008",

doi = "10.4171/ZAA/1343",

language = "English",

volume = "27",

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journal = "Zeitschrift f{\"u}r Analysis und ihre Anwendungen",

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TY - JOUR

T1 - On the Riemann-Hilbert problem with a piecewise constant matrix

AU - Mityushev, Vladimir V.

AU - Rogosin, Sergei

N1 - Mityushev, V. V., Rogosin, S. V. (2008). On the Riemann-Hilbert problem with a piecewise constant matrix. Zeitschrift für Analysis und ihre Anwendungen, 27 (1), 53-66.

PY - 2008

Y1 - 2008

N2 - A constructive solution to the Riemann-Hilbert boundary value problem as well as to the C-linear conjugation problem (or Riemann problem) with a special piecewise constant matrix for a multiply connected domain is obtained. The result is based on a vector generalization of the scalar method of functional equations in complex domain and on application of the Christoffel-Schwarz transformation of the half-plane onto a circular polygon.

AB - A constructive solution to the Riemann-Hilbert boundary value problem as well as to the C-linear conjugation problem (or Riemann problem) with a special piecewise constant matrix for a multiply connected domain is obtained. The result is based on a vector generalization of the scalar method of functional equations in complex domain and on application of the Christoffel-Schwarz transformation of the half-plane onto a circular polygon.

KW - functional equation

KW - FACTORIZATION

KW - multiply connected domain

KW - vector-matrix C-linear conjugation problem

KW - Riemann-Hilbert boundary value problem

KW - Christoffel-Schwarz transformation

UR - http://hdl.handle.net/2160/9317

U2 - 10.4171/ZAA/1343

DO - 10.4171/ZAA/1343

M3 - Article

SN - 0232-2064

VL - 27

SP - 53

EP - 66

JO - Zeitschrift für Analysis und ihre Anwendungen

JF - Zeitschrift für Analysis und ihre Anwendungen

IS - 1

ER -

On the Riemann-Hilbert problem with a piecewise constant matrix

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Keywords

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