The Fan-Taussky-Todd inequalities and the Lumer-Phillips theorem
Classical Analysis and ODEs
2023-05-24 v1
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.
Keywords
Cite
@article{arxiv.2305.14015,
title = {The Fan-Taussky-Todd inequalities and the Lumer-Phillips theorem},
author = {Benedict Bauer and Stefan Gerhold},
journal= {arXiv preprint arXiv:2305.14015},
year = {2023}
}