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arXiv · 2305.14015

The Fan-Taussky-Todd inequalities and the Lumer-Phillips theorem

Benedict Bauer·Stefan Gerhold
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Abstract

We argue that a classical inequality due to Fan, Taussky and Todd (1955) is equivalent to the dissipativity of a Jordan block. As the latter can be characterised via the zeros of Chebyshev polynomials, we obtain a short new proof of the inequality. Three other inequalities of Fan-Taussky-Todd are reproven similarly. By the Lumer-Phillips theorem, the semigroup defined by the Jordan block is contractive. This yields new extensions of the classical Fan-Taussky-Todd inequalities. As an application, we give an estimate for the partial sums of a Bessel function.

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Benedict Bauer, Stefan Gerhold. 2023-05-23. The Fan-Taussky-Todd inequalities and the Lumer-Phillips theorem. https://arxiv.org/abs/2305.14015

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