Perturbation theorems for holomorphic semigroups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

Perturbation theorems for holomorphic semigroups

Authors:

Sebastian Król

Affiliation:

(1) Faculty of Mathematics and Computer Science, Nicolas Copernicus University, UL. Chopina 12/18, 87-100 Torun, Poland

Abstract:

The concept of the gap function is used to give new perturbation results for generators of holomorphic semigroups. In particular, we show that if A is the generator of a holomorphic semigroup on a Banach space and ${M_{A}:=limsup_{|lambda| rightarrow infty, lambda in mathbb {C}_+}|lambda R(lambda , A) |}$ , then every closed linear operator C such that $${(omega,infty)subsetrho(C)}$$

for some

and

$limsup_{lambda rightarrow infty}|lambda R(lambda ,A)- lambda R(lambda ,C)|< frac{1}{2+sqrt{3}}left( 1+ M_{A}^2 right)^{-frac{1}{2}}$

generates a holomorphic semigroup, too. Moreover, we obtain an analogue of this result for differences of semigroups. If T is a holomorphic semigroup and ${k_T:=(limsup_{trightarrow 0^+}|(T(t)+I)^{-1}|)^{-1}}$ , then every C ₀-semigroup S with

$limsuplimits_{trightarrow 0^+}|T(t)-S(t)|< k_T$

is holomorphic. We also give certain estimates for the constants M _A and k _T appearing in the above conditions. The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW grant Nr N201384834.

Keywords:

KeywordHeading" >Mathematics Subject Classification (2000) Primary 47D06 Secondary 47A55

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏