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arXiv · 2401.06635

An elementary approach to splittings of unbounded operators

Arieh Iserles·Karolina Kropielnicka
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Abstract

Using elementary means, we derive the three most popular splittings of $e^{(A+B)}$ and their error bounds in the case when $A$ and $B$ are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups, $e^{tA}$, $e^{tB}$ and $e^{t(A+B)}$. The error of these splittings is bounded in terms of the norm of the commutators $[A, B]$, $[A, [A, B]]$ and $[B, [A, B]]$.

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Arieh Iserles, Karolina Kropielnicka. 2024-01-12. An elementary approach to splittings of unbounded operators. https://arxiv.org/abs/2401.06635

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