The Evolution of Operator Semigroups

2014 ◽  
pp. 3-25 ◽  
Author(s):  
Jerome A. Goldstein ◽  
Rainer Nagel
Keyword(s):  
Operator Semigroups

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

scholarly journals Exponential and polynomial dichotomies of operator semigroups on Banach spaces

2006 ◽  
Vol 175 (2) ◽  
pp. 121-138
Author(s):  
Roland Schnaubelt
Keyword(s):  
Banach Spaces ◽  
Operator Semigroups

On measure of noncompactness and application to global attractors of operator semigroups

2019 ◽  
pp. 1-16
Author(s):  
Ehmet Ablet ◽  
Xiaoling Chen ◽  
Lixin Cheng ◽  
Quanqing Fang ◽  
Zheming Zheng
Keyword(s):  
Measure Of Noncompactness ◽  
Global Attractors ◽  
Operator Semigroups

Exponential Stability Estimate of Fully Nonlinear Aceive Equation by Boundary Control

2011 ◽  
Vol 467-469 ◽  
pp. 1078-1083
Author(s):  
Dian Chen Lu ◽  
Ruo Yu Zhu
Keyword(s):  
Fixed Point ◽  
Exponential Stability ◽  
Dispersion Equation ◽  
Boundary Control ◽  
Existence And Uniqueness ◽  
Stability Estimate ◽  
Banach Fixed Point Theorem ◽  
Operator Semigroups ◽  
Fully Nonlinear ◽  
Well Posed

The well-posed problem for the fully nonlinear Aceive diffusion and dispersion equation on the domain [0, 1] is investigated by using boundary control. The existence and uniqueness of the solutions with the help of the Banach fixed point theorem and the theory of operator semigroups are verified. By using some inequalities and integration by parts, the exponential stability of the fully nonlinear Aceive diffusion and dispersion equation with the designed boundary feedback is also proved.

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