A simple counterexample related to the Lie-Trotter product formula
Claudia Canzi, Graziano Guerra
TL;DR
This paper presents a straightforward counterexample demonstrating that the Lie-Trotter product formula cannot always represent the semigroup generated by the sum of two generators, even if their sum is itself a generator.
Contribution
It provides a simple counterexample showing limitations of the Lie-Trotter product formula in semigroup theory.
Findings
Counterexample invalidates the general applicability of the Lie-Trotter formula
Highlights limitations in representing combined semigroups
Shows that sum of generators does not guarantee formula convergence
Abstract
In this note a very simple example is given which shows that if the sum of two semigroup generators is itself a generator, the generated semigroup in general can not be rapresented by the Lie-Trotter product formula.
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Taxonomy
Topicsadvanced mathematical theories · Quantum chaos and dynamical systems · Spectral Theory in Mathematical Physics