Abstract
This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. De Schepper and F. Sommen, “Introductory Clifford analysis,” in: Operator Theory, Springer, Basel, 2014, pp. 1–27.
R. Fueter, “Die Theorie der regülaren Funktionen einer quaternionen Variablen,” in: Comptes rendus du Congres international des math´emeticiens, Vol. 1, A. W. Broggers, Oslo, 1936.
D. Alpay, M. Shapiro, and D. Volok, “Rational hyperholomorphic functions,” J. of Funct. Anal., 221(1), 122–149 (2005).
A. A. Pogorui and R. M. Rodriguez-Dagnino, “Some algebraic and analytical properties of coquaternion algebra,” Adv. Appl. Clifford Alg., 20, 79–84 (2010).
J. Bory-Reyes and M. Shapiro, “Clifford analysis versus its quaternionic counterparts,” Math. Meth. Appl. Sci., 33(9), 1089–1101 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 3, pp. 365–371 July–September, 2020.
Rights and permissions
About this article
Cite this article
Pogorui, A.A., Kolomiiets, T.Y. Series expansions for monogenic functions in Clifford algebras and their application. J Math Sci 252, 502–507 (2021). https://doi.org/10.1007/s10958-020-05176-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-020-05176-3