Feynman and quasi-Feynman formulas for evolution equations

Abstract

New methods for obtaining representations of solutions of the Cauchy problem for linear evolution equations, i.e., equations of the form u_t'(t, x) = Lu(t, x), where the operator L is linear and depends only on the spatial variable x and does not depend on time t, are proposed. A solution of the Cauchy problem, that is, the exponential of the operator tL, is found on the basis of constructions proposed by the author combined with Chernoff’s theorem on strongly continuous operator semigroups.