Strang's formula for holomorphic semi-groups
In the finite-dimensional case G. Strang proved the following approximation formula \[ \|e^{-t(A+B)}-e^{-tA/2}e^{-tB}e^{-tA/2} \|= O(t^3). \] The authors prove generalizations of this formula to the case of infinite dimensional Banach and unbounded generators \(A,B\). Detailed analysis of Schrödinger operators (\(A=-\Delta, B=V(x)\)) in \(L^p({\mathbb R}^d)\), matrix Schrödinger operator and the pair of elliptic second-order operators (\(A={d\over{dx}}a{d\over{dx}}, A={d\over{dx}}b{d\over{dx}}\)) in \(L^2({\mathbb R}^d)\) is realized.
scientific article; zbMATH DE number 1985994