A New Approach to Slice Regularity on Real Algebras

We expose the main results of a theory of slice regular functions on a real alternative algebra A, based on a well-known Fueter's construction. Our general theory includes the theory of slice regular functions of a quaternionic or octonionic variable and the theory of slice monogenic functions of a Clifford variable. Our approach permits to extend the range of these function theories and to obtain new results. In particular, we show that a fundamental theorem of algebra with multiplicities holds for an ample class of polynomials with coefficients in A. We give several examples to illustrate some interesting aspects of the theory. The original publication is available at www.springerlink.com