Finely differentiable monogenic functions

Roman Lavicka

Mathematical Institute, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic


Since 1970's B. Fuglede and others have been studying finely holomorhic functions, i.e., `holomorphic' functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in \cite{lav2} like a higher dimensional analogue of finely holomorphic functions.