Less than one implies zero

Felix L. Schwenninger; Hans Zwart

doi:10.4064/sm8218-12-2015

Less than one implies zero

Felix L. Schwenninger, Hans Zwart

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

In this paper we show that from an estimate of the form sup_t≥0 C(t) - cos(at)I < 1, we can conclude that C(t) equals cos(at)I. Here (C(t)) t≥0 is a strongly continuous cosine family on a Banach space.

Original language	English
Pages (from-to)	181-188
Number of pages	8
Journal	Studia mathematica
Volume	229
Issue number	2
DOIs	https://doi.org/10.4064/sm8218-12-2015
Publication status	Published - 2015

Keywords

Cosine families
Operator cosine functions
Zero-one-law

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10.4064/sm8218-12-2015

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title = "Less than one implies zero",

abstract = "In this paper we show that from an estimate of the form supt≥0 C(t) - cos(at)I < 1, we can conclude that C(t) equals cos(at)I. Here (C(t)) t≥0 is a strongly continuous cosine family on a Banach space.",

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AU - Zwart, Hans

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AB - In this paper we show that from an estimate of the form supt≥0 C(t) - cos(at)I < 1, we can conclude that C(t) equals cos(at)I. Here (C(t)) t≥0 is a strongly continuous cosine family on a Banach space.

KW - Cosine families

KW - Operator cosine functions

KW - Zero-one-law

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U2 - 10.4064/sm8218-12-2015

DO - 10.4064/sm8218-12-2015

M3 - Article

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VL - 229

SP - 181

EP - 188

JO - Studia mathematica

JF - Studia mathematica

IS - 2

ER -

Less than one implies zero

Abstract

Keywords

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