In this paper the author considers approximations of holomorphic semigroups on general Banach spaces based on A-acceptable rational functions. A general stability theorem is proved. It covers rational functions $r(z)$ with |r(∞ )| = 1 and can be applied even to variable step cases. In particular the question of the Lₚ-stability (p ≠ 2) of Crank-Nicolson schemes for parabolic initial value problems is settled.
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C. Palencia (1993) studied this question.
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