Abstract
In this paper, we consider \(\alpha \)-times resolvent families that are bounded by a given function \({ \varphi }\). We present Hille–Yosida type conditions for an operator to be the generator of a \({ \varphi }\)-bounded \(\alpha \)-times resolvent family. Next, we find some integral estimates on the resolvent of an operator that are sufficient to generate an \(\alpha \)-times resolvent family. We also discuss the effect of perturbation on the generator of such families on their growth.
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Communicated by Jerome A. Goldstein.
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Ghavidel, S.M., Shahali, M. Growth bounds for \(\alpha \)-times resolvent families. Semigroup Forum 107, 109–126 (2023). https://doi.org/10.1007/s00233-023-10372-z
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DOI: https://doi.org/10.1007/s00233-023-10372-z