On polynomials over commutative C*-algebras

The report is devoted to polynomials with continuous complex-valued coefficients. They are called the Weierstrass polynomials.
It is well known, that the study of the Weierstrass polynomials is closely connected with the theory of covering mappings (see, for example, [1–3] and references therein). In particular, there is a class of covering mappings associated with the Weierstrass polynomials. This is the class of so-called polynomial coverings. Moreover, some properties of theWeierstrass polynomials and algebraic equations with continuous coefficients can be formulated in terms of covering mappings, and vice versa.
In the report, we discuss properties of the Weierstrass polynomials over commutative C$^*$-algebras consisting of continuous complex-valued functions defined on compact connected groups.