C－余弦算子函数的谱

Let A be the generator of a C-cosine operator functions C(t) on a Banach space X .The spectrum characterization of (unbounded) cosine operator function C(t)C^-1 on R(C²) is derived. In particular， we characterize the spectrum of strongly continuous cosine operator on a Banach space.     

关于余弦算子函数的一个结果

设Ａ是Ｂａｎａｃｈ空间Ｘ中的闭线性算子,对凡　是单射。文中定义了Ｂａｎａｃｈ空间　范数　强于Ｘ的范数。我们证明了算子Ａ在空间Ｚ中的部分ＡＺ生成Ｚ中的一个余弦算子函数,空间Ｚ具有某种意义上的极大性。     

指数有界的C余弦算子函数

本文引入了指数有界的Ｃ余弦算子函数的生成元，讨论了生成元的基本性质，建立了相应的生成定理、逼近定理及扰动定理．最后给出了指数有界的Ｃ余弦算子函数与指数有界的Ｃ半群的基本联系．     

L~P（Ω）空间余弦算子函数的谱特征

本文得到Ｌ￣Ｐ（Ω）（１＜ｐ＜∞）空间余弦算子函数，用生成元性质表示的谱特征。     

拟分布余弦函数

设X是Banach空间;本文研究了X上定义的拟分布余弦函数2G(φ)G(ψ)=G(φ*ψ)+G(φ(◎)ψ),()ε,ψ∈D;在D上引入了一种新的运算"()"并研究了拟分布余弦函数、积分余弦算子函数和二阶抽象Cauchy问题之间的关系.     

拟分布余弦函数

设X是Banach空间;本文研究了X上定义的拟分布余弦函数:2G（φ）G（Ψ）=G（φ＊Ψ）+G（φ（?）Ψ）,（?）φ,Ψ∈D;在D上引入了一种新的运算“（?）”并研究了拟分布余弦函数、积分余弦算子函数和二阶抽象Cauchy问题之间的关系.     

局部积分余弦算子函数的生成定理

本文讨论局部k次积分Cosine算子函数，在不假定其生成元稠定每件下，建立一个Hille—yosida型定理．     

Banach空间中余弦算子函数生成元的有界性

A是Banach空间X中余弦算子函数C（t),t∈R，和正弦算子函数S（t),t∈R，的生成元。本证明了，对每个f∈C（[0,T];X)，连续函数u,u(t)=∫-tS(t-s)f(s)ds,f∈[0,T]是二阶非齐次0初值问题，u″=Au f的强解的充要条件是：A是空间X中的有界算子。     

On Local Integrated Cosine Functions

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｔｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ,ＸｉｓａＢａｎａｃｈｓｐａｃｅ,ｅｑｕｉｐｐｅｄｗｉｔｈａｎｏｒｍ· ,Ｂ(Ｘ)ｓｔａｎｄｓｆｏｒｔｈｅＢａｎａｃｈａｌｇｅｂｒａｏｆａｌｌｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｏｎＸ ,Ｂ(Ｘ ,Ｙ)ｆｏｒｔｈｅｓｅｔｏｆｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｆｒｏｍＸｔｏａｎｏｔｈｅｒＢａｎａｃｈｓｐａｃｅＹ ,ＡｆｏｒａｃｌｏｓｅｄｏｐｅｒａｔｏｒｏｎＸ ,ρ(Ａ)ｆｏｒｔｈｅｒｅｓｏｌｖｅｎｔｓｅｔｏｆＡ ,Ｄ(Ａ)ｆｏｒｔｈ…     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

板模型具广义边界条件的迁移算子的谱

研究具广义边界条件、非均匀介质、各向异性和连续能量的板模型迁移算子A的谱．证明了K=A-B的相对紧性，在L^1空间研究算子A的谱，以及占优本征值和严格占优本征值．     

反对角算子矩阵及其平方的(ω)性质的摄动

设H为复的无限维可分的Hilbert空间,B(H)为H上的有界线性算子的全体.若σ_a(T)\σ_(ea)(T)=π_(00)(T),则称T∈B(H)满足(ω)性质,其中σ_a(T)和σ_(ea)(T)分别表示算子T的逼近点谱和本质逼近点谱,π_(00)(T)={λ∈isoσ(T):0dimN(T-λI)∞}.T∈B(H)称为满足(ω)性质的摄动,若对任意的紧算子K,T+K满足(ω)性质.本文证明了反对角算子矩阵及其平方具有(ω)性质的摄动的等价性.     

Factorization of Operator Functions in a Hilbert Space

Let be an integer. A Fermat-Euler dynamical system acts on the set of mod- residues coprime to by multiplication by a constant (which is also coprime to ). We study the dependence of the period and the number of orbits of this dynamical system on . Theorems generalizing Fermat's little theorem, as well as empirical conjectures, are given.     

On the Action of a Linear Operator over Sequences in a Banach Space

In this paper we study the action of a bounded linear operator over different kinds of sequences of a Banach space. Our work is mainly devoted to minimal and M - basic sequences. Plans and García Castellón have characterized the boundedness of a linear operator T by requiring the minimality of any sequence whose image is a minimal sequence (e.g. [P, 1969], [GC, 1990]). We extend these results to other types of sequences like M-basic, basic, strong M-basic, etc., We are also interested on conditions that ensure the minimality of the image of a given minimal sequence. Thus in Corollary 3.7 we characterize semi - Fredholm operators as those which transform every p-minimal sequence into q-minimal. In the last section we deal with M - basis whose image is M - basis or norming M - basis or basis or in general the “best” possible sequence.