2017
Том 69
№ 6

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Monogenic functions in a biharmonic algebra

Grishchuk S. V., Plaksa S. A.

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Abstract

We present a constructive description of monogenic functions that take values in a commutative biharmonic algebra by using analytic functions of complex variables. We establish an isomorphism between algebras of monogenic functions defined in different biharmonic planes. It is proved that every biharmonic function in a bounded simply connected domain is the first component of a certain monogenic function defined in the corresponding domain of a biharmonic plane.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 12, pp 1865-1876.

Citation Example: Grishchuk S. V., Plaksa S. A. Monogenic functions in a biharmonic algebra // Ukr. Mat. Zh. - 2009. - 61, № 12. - pp. 1587-1596.

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