Abstract
We define and construct holomorphic $C$-existence families and holomorphic integrated semigroups and discuss their relationships with holomorphic $C$-semigroups and each other. We prove simple Hille-Yosida type theorems, involving the rate of growth of $\lVert(w-A)^{-1}\rVert$ or $\lVert(w-A)^{-1}C\rVert$ in a sector, for an operator to generate any of these families of operators.
Citation
Ralph deLAUBENFELS. "Holomorphic $C$-Existence Families." Tokyo J. Math. 15 (1) 17 - 38, June 1992. https://doi.org/10.3836/tjm/1270130249
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