Abstract
For an arbitrary bounded linear operator $C$, on a Banach space, and a closable linear operator $A$, we introduce a $C$-regularized semigroup for $A$. We present equivalences between $A$ having a $C$-regularized semigroup, the corresponding abstract Cauchy problem, well-posedness on a continuously embedded subspace, and (for exponentially bounded $C$-regularized semigroups) the Laplace transform.
Citation
Guo Zheng Sun. Sheng Wang Wang. Ralph deLaubenfels. "Regularized semigroups, existence families and the abstract Cauchy problem." Differential Integral Equations 8 (6) 1477 - 1496, 1995. https://doi.org/10.57262/die/1368638176
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