Semigroups of operators and abstract dynamic equations on time scales
Semigroups of operators and abstract dynamic equations on time scales
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DOI：
10.1016/j.amc.2015.07.110
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发表时间：
2015-11
期刊：
影响因子：
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通讯作者：
A. Hamza;K. Oraby
中科院分区：
文献类型：
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作者：
A. Hamza;K. Oraby
本文将Banach空间X中的有界线性算子的强连续半群(C0-半群)理论推广到其自身。建立了C0半群{T(T)：T∈T}及其生成元A的许多性质.这里T⊆R≥0是一个具有加性半群结构的时标。我们还建立了动态初值问题{xΔ(T)=Ax(T)，t∈Tx(0)=x0∈D(A)，0∈T有唯一解的充要条件，其中D(A)是A的区域。最后，我们统一了连续的Hille-Yosida-Phillips定理和离散的Gibson定理。
In this paper we develop the theory of strongly continuous semigroups (C 0-semigroups) of bounded linear operators from a Banach space X into itself. Many properties of a C 0-semigroup {T (t): t∈ T} and its generator A are established. Here T⊆ R≥ 0 is a time scale endowed with an additive semigroup structure. We also establish necessary and sufficient conditions for the dynamic initial value problem {x Δ (t)= A x (t), t∈ T x (0)= x 0∈ D (A), 0∈ T to have a unique solution, where D (A) is the domain of A. Finally, we unify the continuous Hille–Yosida–Phillips Theorem and the discrete Gibson Theorem.