The problem of regularizing infinite products is a long standing one in mathematical and theoretical physics, as well as in mathematics, of course. Several either formal or rigorous techniques have been introduced. One that obtained an undiscussed favor is the zeta regularization. The idea is simple to write down in a formal way (so as it as been used for a long times by physicists), and has go...

Let (A, G, alpha) be a partial dynamical system. We show that there is a bijective corespondence between Ginvariant ideals of A and ideals in the partial crossed prroduct A xalpha, r G provided the action is exact and residually topologically free.

In [Linear Algebra Appl., 161:227{263, 1992] the LCP-property of a nite set of square complex matrices was introduced and studied. A set is an LCP-set if all left in nite products formed from matrices in are convergent. It was shown earlier in [Linear Algebra Appl., 130:65{82, 1990] that a set paracontracting with respect to a xed norm is an LCP-set. Here a converse statement is proved: If is a...

An algorithm is introduced and shown to lead to a unique infinite product representation for a given formal power series A(z) with A(O)= 1. The infinite product is 1; n (1 + b,z'n)> " =I

We study analytic properties of certain infinite products of cyclotomic polynomials that generalize some introduced by Mahler. We characterize those that have the unit circle as a natural boundary and use associated Dirichlet series to obtain their asymptotic behavior near roots of unity.