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Estimates on Strang’s formula. (Estimations sur la formule de Strang.) (French. Abridged English version) Zbl 0827.47034
Summary: Let $$a$$, $$b$$, $$a_0$$, $$b_0$$ be positive functions of class $$C^\infty$$ on $$\mathbb{T}^2= (\mathbb{R}/ \mathbb{Z})^2$$. The operators $A= {\textstyle {\partial \over {\partial x}} a {\partial \over {\partial x}}}- a_0 \qquad \text{and} \qquad B= {\textstyle {\partial \over {\partial y}} b {\partial \over {\partial y}}}- b_0$ generate holomorphic semi-groups in $$L^2 (\mathbb{T}^2)$$ denoted by $$e^{tA}$$ and $$e^{tB}$$. We prove that there exists a constant $$c$$ such that $|e^{t(A+ B)}- e^{t a/2} e^{tB} e^{t A/2} |_{{\mathcal L} (L^2 (\mathbb{T}^2))}\leq ct.$ This estimate implies stability for a class of extrapolations of Strang’s formula.

##### MSC:
 47D06 One-parameter semigroups and linear evolution equations 47A60 Functional calculus for linear operators