渐近概周期序列离散半群与空间的一致指数稳定性

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2015-10-29 DOI:10.4171/ZAA/1550

Nisar Ahmad, Habiba Khalid, A. Zada

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引用次数: 4

摘要

证明离散半群T = {T (n): n∈Z+}是一致指数稳定的当且仅当对于每个Z (n)∈AAP0(Z+，X)柯西问题{yn+1 = T (1)yn + Z (n +1)， y(0) = 0的解属于AAP0(Z+，X)。其中T(1)是T的代数生成器，Z+是所有非负整数的集合，X是复巴拿赫空间。我们的证明使用离散演化半群的方法。

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Uniform Exponential Stability of Discrete Semigroup and Space of Asymptotically Almost Periodic Sequences

We prove that the discrete semigroup T = {T (n) : n ∈ Z+} is uniformly exponentially stable if and only if for each z(n) ∈ AAP0(Z+,X ) the solution of the Cauchy problem { yn+1 = T (1)yn + z(n + 1), y(0) = 0 belongs to AAP0(Z+,X ). Where T (1) is the algebraic generator of T, Z+ is the set of all non-negative integers and X is a complex Banach space. Our proof uses the approach of discrete evolution semigroups.

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.