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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.

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