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 given by the Lie--Trotter product formula.
Canzi, C., Guerra, G. (2012). A simple counterexample related to the Lie–Trotter product formula. SEMIGROUP FORUM, 84(3), 499-504 [10.1007/s00233-011-9326-6].
A simple counterexample related to the Lie–Trotter product formula
GUERRA, GRAZIANO
2012
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 given by the Lie--Trotter product formula.
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