# 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

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topS. 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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- [7] Mel’nichenko, I. P., The representation of harmonic mappings by monogenic functions, Ukrainian Math. J. 27, no. 5 (1975), 499-505.
- [8] Mel’nichenko, I. P., Algebras of functionally invariant solutions of the threedimensionalLaplace equation, Ukrainian Math. J. 55, no. 9 (2003), 1551-1559.
- [9] Mel’nichenko, I. P., Plaksa, S. A., Commutative algebras and spatial potential fields, Inst. Math. NAS Ukraine, Kiev, 2008 (Russian).
- [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] 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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