Geodesic
Local $K$-Convoluted $C$-groups and Abstract Cauchy Problems
Kragujevac Journal of Mathematics, Tome 48 (2024) no. 5, p. 655 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We first present a new form of a local $K$-convoluted $C$-group on a Banach space $X$, and then deduce some basic properties of a nondegenerate local $K$-convoluted $C$-group on $X$ and some generation theorems of local $K$-convoluted $C$-groups, which can be applied to obtain some equivalence relations between the generation of a nondegenerate local $K$-convoluted $C$-group on $X$ with subgenerator $A$ and the unique existence of solutions of the abstract Cauchy problem $\text{ACP}(A,f,x)$.
Classification : 47D60, 47D62
Keywords: local K-convoluted C-group, generator, subgenerator, abstract Cauchy problem 
@article{KJM_2024_48_5_a0,
     author = {Chung-Cheng Kuo},
     title = {Local $K${-Convoluted} $C$-groups and {Abstract} {Cauchy} {Problems}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {655 },
     year = {2024},
     volume = {48},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2024_48_5_a0/}
}
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Chung-Cheng Kuo. Local $K$-Convoluted $C$-groups and Abstract Cauchy Problems. Kragujevac Journal of Mathematics, Tome 48 (2024) no. 5, p. 655 . http://geodesic.mathdoc.fr/item/KJM_2024_48_5_a0/