Convergence estimates for the Magnus expansion I. Banach algebras

2017/09/06 by Gyula Lakos, Lakos, Gyula
Mathematics · #16W60 #16W80 #46H30 #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1709.01791

openalex publication_date 2017/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 C₂=2.89847930…. More generally, the resolvent method is developed in the analytic setting.

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