Schwarz Problem for J-Analytic Functions in an Ellipse View Full Text


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Article Info

DATE

2022-07

AUTHORS

V. G. Nikolaev

ABSTRACT

The Schwarz problem for functions analytic in the sense of Douglis in an ellipse is considered. Necessary and sufficient conditions on the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell \times \ell $$\end{document} matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} and the ellipse \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} are obtained under which the Schwarz problem has a unique solution in Hölder classes. In the case of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell = 2$$\end{document} and matrices with distinct eigenvalues, the Schwarz problem is reduced to a scalar functional equation. Sufficient conditions on a Jordan basis of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} are obtained under which the Schwarz problem is solvable in an arbitrary ellipse. Matrices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} with eigenvalues lying above and below the real line are considered. More... »

PAGES

1089-1111

References to SciGraph publications

  • 2006-02. Hyperanalytic Functions and Their Applications in JOURNAL OF MATHEMATICAL SCIENCES
  • 2013-07-29. Pseudo-Differential Equations on Manifolds with Non-smooth Boundaries in DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATIONS
  • 2019-04-26. A Class of Orthogonal Polynomials on the Boundary of an Ellipse in JOURNAL OF MATHEMATICAL SCIENCES
  • 1982. Fourier Series, A Modern Introduction Volume 2 in NONE
  • 2015-07. On the solution of the Schwarz problem for J-analytic functions in a domain bounded by a Lyapunov contour in DIFFERENTIAL EQUATIONS
  • 2011-02-08. The Schwarz problem for Douglis analytic functions in JOURNAL OF MATHEMATICAL SCIENCES
  • 2013-11-07. General boundary value problems for pseudo-differential equations and related difference equations in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2017-10. Schwarz problem for first-order elliptic systems on the plane in DIFFERENTIAL EQUATIONS
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    http://scigraph.springernature.com/pub.10.1134/s0965542522050104

    DOI

    http://dx.doi.org/10.1134/s0965542522050104

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