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We study mild n times integrated C-existence families without the assumption of exponential boundedness. We present several equivalent conditions for these families. Hille-Yosida type necessary and sufficient conditions are given for the exponentially bounded case.
We extend some recent results for regularized semigroups to strongly continuous n-times integrated C-cosine operator functions. Several equivalent conditions for the existence and uniqueness of solutions of (ACP) are also presented.
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