A Laplace transform approach to $C$-semigroups on a $\mathcal{T}_{\varepsilon, λ}$-complete random normed module
Year: 2025
Type: preprint
Abstract: In this paper, we first introduce the notion of the Laplace transform for an abstract-valued function from $[0, \infty)$ to a $\mathcal{T}_{\varepsilon, λ}$-complete random normed module $S$. Then, combining respective advantages of the $(\varepsilon, λ)$-topology and the locally $L^0$-convex topology on $S$, we prove the differentiability, Post-Widder inversion formula and uniqueness of such a Laplace transform. Second, based on the above work, we establish the Hille-Yosida theorem for an exponentially bounded $C$-semigroup on $S$, considering both the dense and nondense cases of the range of $C$, respectively, which extends and improves several important results. Finally, we also apply such a Laplace transform to abstract Cauchy problems in the random setting.
Source: arXiv (Cornell University)
Authors: Zhang, Xia, Wei, Leilei, Liu, Ming
Institution: Tiangong University
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6357943783
OpenAlex ID: W4416083871
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