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.
Keywords
copolynomial, \(\delta\)-function, formal power series, multiplication of copolynomials, formal functional calculus
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PDFDOI: http://dx.doi.org/10.12958/adm2352
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