Constructive description of monogenic functions in finite-dimensional commutative algebras

TitleConstructive description of monogenic functions in finite-dimensional commutative algebras
Publication TypeJournal Article
Year of Publication2015
AuthorsShpakivskyi, VS
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.04.023
Issue4
SectionMathematics
Pagination23-28
Date Published4/2015
LanguageUkrainian
Abstract

We obtain a constructive description of monogenic functions taking values in an arbitrary finite-dimensional commutative associative algebra with unity with the help of holomorphic functions of the complex variable.

Keywordsconstructivity, finite-dimensional commutative algebras, monogenic functions
References: 

1.    Segre C. Math. Ann., 1892, 40: 413–467. https://doi.org/10.1007/BF01443559
2.    Ringleb F. Rend. Circ. Mat. Palermo, 1933, 57, No 1: 311–340. https://doi.org/10.1007/BF03017582
3.    Riley J. D. Tohoku Math. J.,1953, 5, No 2: 132–165. https://doi.org/10.2748/tmj/1178245302
4.    Ketchum P.W. Trans. Amer. Math. Soc., 1928, 30, No 4: 641–667. https://doi.org/10.1090/S0002-9947-1928-1501452-7
5.    Melnichenko I. P. Ukr. math. zhurn., 1975, 27, No 5: 606–613 (in Russian).
6.    Melnichenko I. P., Plaksa S. A. Commutative algebras and spatial potential fields, Kiev: Institute of Mathematics the NAS of Ukraine, 2008 (in Russian).
7.    Plaksa S. A., Shpakovskii V. S. Ukr. math. zhurn., 2010, 62, No 8: 1078–1091 (in Russian).
8.    Plaksa S. A., Pukhtaevich R. P. Ukr. math. zhurn., 2013, 65, No 5: 670–680 (in Russian).
9.    Pukhtaievych R. P. Zb. Pr. Inst. Mat. NAN Ukraine, 2013, 10, No 4–5: 352-361.
10.    Shpakivskyi V. S., Plaksa S. A. Bull. Soc. Sci. Lett. Lod´z, 2010, 60: 47–54.
11.    Plaksa S. A. In: Advances in Applied Analysis, Trends in Mathematics. – Basel: Springer, 2012: 177–223. https://doi.org/10.1007/978-3-0348-0417-2_5
12.    Plaksa S. A., Shpakivskyi V. S. J. Algerian Math. Soc., 2014, 1: 1–13.
13.    Plaksa S. A., Pukhtaievych R. P. An. St. Univ. Ovidius Constanta. – 2014, 22, No 1: 221–235.
14.    Cartan E. Ann. fac. sci. Toulouse, 1898, 12, No 1: 1–64. https://doi.org/10.5802/afst.143
15.    Hille E., Phillips R. Functional analysis and semi-groups, Moscow: Izd-vo Inostr. lit., 1962 (in Russian).