本文選題：預(yù)解正算子 + 譜分布　； 參考：《數(shù)學(xué)的實(shí)踐與認(rèn)識(shí)》2017年02期

【摘要】：研究了兩相同部件溫儲(chǔ)備可修的人機(jī)系統(tǒng),運(yùn)用C_0半群的相關(guān)理論,對(duì)系統(tǒng)主算子的譜界進(jìn)行估值.估算系統(tǒng)的算子產(chǎn)生的半群的增長(zhǎng)界,然后運(yùn)用了共尾的概念及相關(guān)的理論,得到了系統(tǒng)算子A+B的譜界與系統(tǒng)算子產(chǎn)生的半群的增長(zhǎng)界相同.進(jìn)而運(yùn)用相關(guān)代數(shù)知識(shí)證得,0為系統(tǒng)算子的簡(jiǎn)單本征值,并分析了系統(tǒng)算子的譜分布,得到系統(tǒng)的指數(shù)穩(wěn)定性.并研究了系統(tǒng)算子預(yù)解式的特性.對(duì)任意給定的δ0,γ=a+bi,-μ+δa_1≤a≤a_2,得到lim|b|→∞‖R(γ;A+B)‖=0.進(jìn)而得到在~sRγ≥a_1的右半平面內(nèi)相應(yīng)于系統(tǒng)算子A+B的譜點(diǎn)由有限個(gè)本征值組成.
[Abstract]:In this paper, the repairable man-machine system with two same components is studied, and the spectral bound of the main operator of the system is estimated by using the theory of C _ s _ 0 semigroup. The growth bounds of Semigroups generated by system operators are estimated. Then by using the concept of cotail and related theories, the spectral bounds of system operators A B and the growth bounds of Semigroups generated by system operators are obtained. Then we prove that 0 is the simple eigenvalue of the system operator by using the knowledge of correlation algebra. The spectral distribution of the system operator is analyzed and the exponential stability of the system is obtained. The properties of the resolvent of the system operator are studied. For any given 未 _ 0, 緯 -a bibior- 渭 未 _ a _ s _ 1 鈮，

本文編號(hào)：1917893