Trotter-type formula for operator semigroups on product spaces
| Autor: | Stephan, Artur |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Strongly continuous semigroups of linear operators
inhomogeneous abstract Cauchy problems Trotter-product formula FOS: Physical sciences Mathematical Physics (math-ph) operator-norm convergence rate estimate tensor space Functional Analysis (math.FA) Mathematics - Functional Analysis block operator matrices Mathematics - Classical Analysis and ODEs product space 15A60 Classical Analysis and ODEs (math.CA) FOS: Mathematics 47D06 47D06 15A60 split-step method Mathematical Physics time discretization |
| DOI: | 10.48550/arxiv.2307.00419 |
| Popis: | We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the classical Trotter-product formula, the approximation is given by freezing subsequently the components of each subspace. After deriving necessary stability estimates for the approximation, which immediately provide convergence in the natural strong topology, we investigate convergence in the operator norm. The main result shows that an almost optimal convergence rate can be established if the dominant operator generates a holomorphic semigroup and the off-diagonal coupling operators are bounded. |
| Databáze: | OpenAIRE |
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