Monogenic functions in a biharmonic algebra

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


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.
How to Cite
Gryshchuk, S. V., and S. A. Plaksa. “Monogenic Functions in a Biharmonic Algebra”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 12, Dec. 2009, pp. 1587-96,
Research articles