The Cauchy problem for Schroedinger type equations with variable coefficients

摘要

We assume that a_(jk)(x) belong to B~∞ and b_j(t,x),c(t,x) are in C~0([0, T];B~∞), where B~∞ stands for the set of complex valued functions defined in R~n whose all derivatives are bounded in R~n. For a topological space X, a non negative integer k and an interval I in R~1 we denote by C~k(Ⅰ;Ⅹ) the set of functions k times continuously differentiable with respect to t ∈ I in the topology of X.