Monogenic functions in a biharmonic algebra

  • S. V. Gryshchuk
  • S. A. Plaksa Ин-т математики НАН Украины, Киев

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.
Published
25.12.2009
How to Cite
GryshchukS. V., and PlaksaS. A. “Monogenic Functions in a Biharmonic Algebra”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 12, Dec. 2009, pp. 1587-96, https://umj.imath.kiev.ua/index.php/umj/article/view/3125.
Section
Research articles