Abstract
The weakening of conditions imposed on the solution operators of the Cauchy problem for abstract first- and second-order differential equations has led (see (1-3)) to the notion of integrated semigroup and integrated cosine function. In the present paper, we derive formulas relating the integrated cosine function to the solution operator Yk(t) of the Cauchy problem u �� (t )+ k t u � (t )= Au(t) ,t >0, (1)
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