On close-to-scalar one-parameter cosine families

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:429

Article

Bobrowski, Adam¹  Chojnacki, Wojciech^2,3  Gregosiewicz, Adam¹ 

[1] Lublin Univ Technol, Fac Elect Engn & Comp Sci, Dept Math, PL-20618 Lublin, Poland

[2] Univ Adelaide, Sch Comp Sci, Adelaide, SA 5005, Australia

[3] Cardinal Stefan Wyszynski Univ, Coll Sci, Fac Math & Nat Sci, PL-01815 Warsaw, Poland

关键词: Cosine family;    Normed algebra;    Scalar element;   

DOI  :  10.1016/j.jmaa.2015.04.012

来源: Elsevier

【 摘 要 】

It is shown that if two cosine families with values in a normed algebra with unity, both indexed by t running over all real numbers, of which one consists of the multiples of the unity of the algebra by numbers of the form cos at for some real a, differ in norm by less than 8/(3 root 3) uniformly in t, then these families coincide. For a not equal 0, the constant 8/(3 root 3) is optimal and cannot be replaced by any larger number. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free