Formal functional calculus for copolynomials over a commutative ring

Abstract

We study the copolynomials, i.e. \(K\)-linear mappings from the ring of polynomials \(K[x_1,...,x_n]\) into the commutative ring \(K\). With the help of the Cauchy-Stieltjes transform of a copolynomial we introduce and study a multiplication of copolynomials. We build a counterpart of formal functional calculus for the case of a finite number of copolynomials. We obtain an analogue of the spectral mapping theorem and analogues of the Taylor formula and the Riesz-Dunford formula.