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2013 | 67 | 1 |
Tytuł artykułu

On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
67
Numer
1
Opis fizyczny
Daty
wydano
2013
online
2015-07-15
Twórcy
Bibliografia
  • Davydov, N. A., The continuity of an integral of Cauchy type in a closed domain, Dokl. Akad. Nauk SSSR 64, no. 6 (1949), 759–762 (Russian).
  • Salaev, V. V., Direct and inverse estimates for a singular Cauchy integral along a closed curve, Mat. Zametki 19, no. 3 (1976), 365–380 (Russian).
  • Gerus, O. F., Finite-dimensional smoothness of Cauchy-type integrals, Ukrainian Math. J. 29, no. 5 (1977), 490–493.
  • Gerus, O. F., Some estimates of moduli of smoothness of integrals of the Cauchy type, Ukrainian Math. J. 30, no. 5 (1978), 594–601.
  • Ketchum, P. W., Analytic functions of hypercomplex variables, Trans. Amer. Math. Soc. 30 (1928), 641–667.
  • Kunz, K. S., Application of an algebraic technique to the solution of Laplace’s equation in three dimensions, SIAM J. Appl. Math. 21, no. 3 (1971), 425–441.
  • Mel’nichenko, I. P., The representation of harmonic mappings by monogenic functions, Ukrainian Math. J. 27, no. 5 (1975), 499–505.
  • Mel’nichenko, I. P., Algebras of functionally invariant solutions of the threedimensional Laplace equation, Ukrainian Math. J. 55, no. 9 (2003), 1551–1559.
  • Mel’nichenko, I. P., Plaksa, S. A., Commutative algebras and spatial potential fields, Inst. Math. NAS Ukraine, Kiev, 2008 (Russian).
  • Plaksa, S. A., Riemann boundary-value problem with infinite index of logarithmic order on a spiral contour. I, Ukrainian Math. J. 42, no. 11 (1990), 1509–1517.
  • Shpakivskyi, V. S., Plaksa, S. A., Integral theorems and a Cauchy formula in a commutative three-dimensional harmonic algebra, Bull. Soc. Sci. Lett. Łódz Ser. Rech. Deform. 60 (2010), 47–54.
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Bibliografia
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bwmeta1.element.ojs-doi-10_17951_a_2013_67_1_57-64
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