标题：Exponential dichotomy on time scales and admissibility of the pair ( C rd b ( T + , X ) , L p ( T + , X ) ) $(\mathrm{C}_{\mathrm{rd}}^{b}(\mathbb{T}^{+}, X),L^{p}(\mathbb{T}^{+},X))$
摘要：In this paper, we study a relation between exponential dichotomy on time scales and admissibility of the pair ( C rd b ( T + , X ) , L p ( T + , X ) ) $(\mathrm{C}_{\mathrm{rd}}^{b}(\mathbb{T}^{+}, X),L^{p}(\mathbb{T}^{+},X))$ for an evolution family on time scales. We establish a sufficient criterion for the existence of exponential dichotomy on time scales in terms of the admissibility of the pair ( C rd b ( T + , X ) , L p ( T + , X ) ) $(\mathrm{C}_{\mathrm{rd}}^{b}(\mathbb{T}^{+}, X),L^{p}(\mathbb{T}^{+},X))$ for the evolution family. Conversely, with the help of exponential dichotomy on time scales, we give the admissibility of the pair ( C rd b ( T + , X ) , L p ( T + , X ) ) $(\mathrm{C}_{\mathrm{rd}}^{b}(\mathbb{T}^{+}, X),L^{p}(\mathbb{T}^{+},X))$ for an input-output equation on time scales.
