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Strang’s formula for holomorphic semi-groups. (English) Zbl 1030.35095
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.

35K15 Initial value problems for second-order parabolic equations
47D06 One-parameter semigroups and linear evolution equations
35A35 Theoretical approximation in context of PDEs
Full Text: DOI
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