Convergence estimates for the Magnus expansion I. Banach algebras

Gyula Lakos

Convergence estimates for the Magnus expansion I. Banach algebras

Functional Analysis 2025-01-03 v5 Rings and Algebras

Authors: Gyula Lakos

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.

Keywords

Magnus expansion Banach algebras convergence estimates Baker-Campbell-Hausdorff series resolvent method convergence radius

Cite

@article{arxiv.1709.01791,
  title  = {Convergence estimates for the Magnus expansion I. Banach algebras},
  author = {Gyula Lakos},
  journal= {arXiv preprint arXiv:1709.01791},
  year   = {2025}
}

Comments

Part I of original submission arXiv:1709.01791v1, rewritten and expanded

Convergence estimates for the Magnus expansion I. Banach algebras

Abstract

Keywords

Cite

Comments

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