Less than one implies zero

Felix L. Schwenninger; Hans Zwart

Studia Mathematica, Tome 231 (2015), p. 181-188 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper we show that from an estimate of the form $s u p_{t \geq 0} | | C (t) - c o s (a t) I | | < 1$ , we can conclude that C(t) equals cos(at)I. Here ${(C (t))}_{t \geq 0}$ is a strongly continuous cosine family on a Banach space.

Publié le : 2015-01-01

Zbl 1337.47063

EUDML-ID : urn:eudml:doc:285921

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     author = {Felix L. Schwenninger and Hans Zwart},
     title = {Less than one implies zero},
     journal = {Studia Mathematica},
     volume = {231},
     year = {2015},
     pages = {181-188},
     zbl = {1337.47063},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8218-12-2015}
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Felix L. Schwenninger; Hans Zwart. Less than one implies zero. Studia Mathematica, Tome 231 (2015) pp. 181-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8218-12-2015/