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In this note, we formulate a theorem giving bounds on the powers of linear operators, in a general Banach space setting. The relevance of the theorem is illustrated by applying it to the Crank-Nicholson method for the numerical solution of the heat equation. This application yields a stability estimate in the maximum norm which amounts to an improvement… (More)

We establish the positive definiteness of some functions and of some matrices that arise as solutions of generalized Lyapunov equations.

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