English

Convergence estimates for the Magnus expansion IIA. $2\times2$ matrices with operator norm

Spectral Theory 2023-04-10 v1 Classical Analysis and ODEs

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 IIA, we investigate the case of 2×22\times2 matrices with respect to the operator norm. We consider norm estimates and minimal presentations in terms of the Magnus and BCH expansions. Some results are obtained in the complex case, but a more complete picture is obtained in the real case.

Keywords

Cite

@article{arxiv.2304.03513,
  title  = {Convergence estimates for the Magnus expansion IIA. $2\times2$ matrices with operator norm},
  author = {Gyula Lakos},
  journal= {arXiv preprint arXiv:2304.03513},
  year   = {2023}
}

Comments

Part II/2 of original submission arXiv:1709.01791, expanded. arXiv admin note: text overlap with arXiv:1910.03328