2018 | OriginalPaper | Buchkapitel
Generalized backward shift operators on the ring ℤ[[x]], Cramer’s rule for infinite linear systems, and p-adic integers
verfasst von : Sergey Gefter, Anna Goncharuk
Erschienen in: The Diversity and Beauty of Applied Operator Theory
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Let A be a generalized backward shift operator on ℤ[[x]] and f(x) be a formal power series with integer coefficients. A criterion for the existence of a solution of the linear equation (Ay)(x) + f(x) = y(x) in ℤ[[x]] is obtained. An explicit formula for its unique solution in ℤ[[x]] is found as well. The main results are based on using the p-adic topology on ℤ and on using a formal version of Cramer’s rule for solving infinite linear systems.