The correctness of Cauchy problem for a polynomial difference operator is studied. An easily verifiable sufficient condition for correctness of a two-dimensional Cauchy problem for an operator with constant coefficients is proved.
We define a derivation of the ring of Laurent series with supports in rational cones and prove existence and uniqueness of a solution to an analog of one initial-boundary value problem of Hörmander for polynomial differential operators with constant coefficients in the class of formal Laurent series.
In this paper, the initial-boundary value problem of Hormander is formulated in the class of functions representable by Laurent series supported in rational cones. Using the Borel transformation of Laurent series we establish a connection between a differential and a difference problems and prove its global analytic solvability
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.