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arXiv · 1709.01791

Convergence estimates for the Magnus expansion I. Banach algebras

Gyula Lakos
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Abstract

We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff expansion are also made. In this Part I, we consider the general Banach algebraic setting. We show that the (cumulative) convergence radius of the Magnus expansion is $2$; and of the Baker--Campbell--Hausdorff series is $\mathrm C_2=2.89847930\ldots$. More generally, the resolvent method is developed in the analytic setting.

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Gyula Lakos. 2017-09-06. Convergence estimates for the Magnus expansion I. Banach algebras. https://arxiv.org/abs/1709.01791

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