PROPERTIES OF CLASSES OF SLICE ENTIRE FUNCTIONS AND SLICE HOLOMORPHIC IN THE UNIT BALL FUNCTIONS
In the paper we investigate properties of class of slice entire functions of several complex variables i.e. these functions are entire on every slice {z^0+tb: tC} for an arbitrary z^0C^n and for the fixed direction bC^n{0}. For a function F from this class we consider a slice function g_z(t)=F(z+tb) (zC^n, tC) and a directional derivative _b F(z):=g’_z(0), ^p_b F(z):=_b (_b ^p-1F(z)), p2. We show that if a function F belongs to this class then for any pN the function _b ^p F also belongs to the class. A similar results is also obtained for functions which are slice holomorphic in the unit ball. , number=16(60), journal=PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, author=Bandura А. І. and Shegda, L. M., year=2021, month=Oct., pages=7–10