A NOTE ON THE SHARPNESS OF NONOPTIMAL COMPARISON RATES FOR ＄C_{0}＄ -SEMIGROUPS
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概要
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If ＄￥alpha￥in(0,1)＄ is given and ＄T_{1}=￥{T_{1}(t);t￥geq 0￥},＄ ＄T_{2}=￥{T_{2}(t);t￥geq 0￥}＄ are ＄C_{0}＄-semigroups defined on a real Banach space (X, ＄|￥cdot|＄ ), we indicate sufficient conditions for the existence of ＄x_{￥alpha}￥in X＄ such that |T_{1}(t)x_{￥alpha}-T_{2}(t)x_{￥alpha}|=O(t^{￥alpha})＄ and ＄|T_{1}(t)x_{￥alpha}-T_{2}(t)x_{￥alpha}|￥neq o(t^{￥alpha})＄ as t￥rightarrow 0+＄ , that is, for which the approximation rate ＄O(t^{￥alpha})＄ is sharp.
- Yokohama City University and Yokohama National Universityの論文
- 2004-00-00
Yokohama City University and Yokohama National University | 論文
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