87 research outputs found
Convergence estimates for the Magnus expansion I. Banach algebras
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 ; and of the Baker--Campbell--Hausdorff
series is .Comment: Part I of original submission arXiv:1709.01791v1, rewritten and
expande
Spectral calculations on locally convex vector spaces I
We develop a holomorphic functional calculus for (multivalued linear)
operators on locally convex vector spaces. This includes the case of fractional
powers along Lipschitz curves.Comment: 18 page
Factorization of Laurent series over commutative rings
We generalize the Wiener-Hopf factorization of Laurent series to more general
commutative coefficient rings, and we give explicit formulas for the
decomposition. We emphasize the algebraic nature of this factorization.Comment: 8 page
Convergence estimates for the Magnus expansion II. -algebras
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 II, we prove
growth estimates regarding the Magnus expansion in the setting Hilbert space
operators near the critical cumulative norm . We also conduct a detailed
geometrical study in the case of real matrices, leading to some
special normal forms via the Magnus expansion.Comment: Part II of original submission arXiv:1709.01791v1, basically
unrewritte
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