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

S. A. Plaksa; V. S. Shpakivskyi

Annales UMCS, Mathematica (2013)

  • Volume: 67, Issue: 1, page 57-64
  • ISSN: 2083-7402

Abstract

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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.

How to cite

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S. A. Plaksa, and V. S. Shpakivskyi. "On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical." Annales UMCS, Mathematica 67.1 (2013): 57-64. <http://eudml.org/doc/268298>.

@article{S2013,
abstract = {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.},
author = {S. A. Plaksa, V. S. Shpakivskyi},
journal = {Annales UMCS, Mathematica},
keywords = {Three-dimensional harmonic algebra; Cauchy type integral; limiting values; closed Jordan rectifiable curve; three-dimensional harmonic algebra; rectifiable Jordan curve},
language = {eng},
number = {1},
pages = {57-64},
title = {On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical},
url = {http://eudml.org/doc/268298},
volume = {67},
year = {2013},
}

TY - JOUR
AU - S. A. Plaksa
AU - V. S. Shpakivskyi
TI - On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical
JO - Annales UMCS, Mathematica
PY - 2013
VL - 67
IS - 1
SP - 57
EP - 64
AB - 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.
LA - eng
KW - Three-dimensional harmonic algebra; Cauchy type integral; limiting values; closed Jordan rectifiable curve; three-dimensional harmonic algebra; rectifiable Jordan curve
UR - http://eudml.org/doc/268298
ER -

References

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  1. [1] 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). Zbl0041.39707
  2. [2] Salaev, V. V., Direct and inverse estimates for a singular Cauchy integral along aclosed curve, Mat. Zametki 19, no. 3 (1976), 365-380 (Russian). Zbl0345.44006
  3. [3] Gerus, O. F., Finite-dimensional smoothness of Cauchy-type integrals, Ukrainian Math. J. 29, no. 5 (1977), 490-493. Zbl0429.30035
  4. [4] Gerus, O. F., Some estimates of moduli of smoothness of integrals of the Cauchy type, Ukrainian Math. J. 30, no. 5 (1978), 594-601. Zbl0411.30026
  5. [5] Ketchum, P. W., Analytic functions of hypercomplex variables, Trans. Amer. Math. Soc. 30 (1928), 641-667.[Crossref] Zbl55.0787.02
  6. [6] Kunz, K. S., Application of an algebraic technique to the solution of Laplace’s equationin three dimensions, SIAM J. Appl. Math. 21, no. 3 (1971), 425-441.[Crossref] Zbl0235.31007
  7. [7] Mel’nichenko, I. P., The representation of harmonic mappings by monogenic functions, Ukrainian Math. J. 27, no. 5 (1975), 499-505. 
  8. [8] Mel’nichenko, I. P., Algebras of functionally invariant solutions of the threedimensionalLaplace equation, Ukrainian Math. J. 55, no. 9 (2003), 1551-1559. 
  9. [9] Mel’nichenko, I. P., Plaksa, S. A., Commutative algebras and spatial potential fields, Inst. Math. NAS Ukraine, Kiev, 2008 (Russian). 
  10. [10] Plaksa, S. A., Riemann boundary-value problem with infinite index of logarithmicorder on a spiral contour. I, Ukrainian Math. J. 42, no. 11 (1990), 1509-1517. Zbl0719.30029
  11. [11] Shpakivskyi, V. S., Plaksa, S. A., Integral theorems and a Cauchy formula in a commutativethree-dimensional harmonic algebra, Bull. Soc. Sci. Lett. Łodź S´er. Rech. D´eform. 60 (2010), 47-54. Zbl1229.30026

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