## Tokyo Journal of Mathematics

### Holomorphic $C$-Existence Families

Ralph deLAUBENFELS

#### 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.

#### Article information

Source
Tokyo J. Math., Volume 15, Number 1 (1992), 17-38.

Dates
First available in Project Euclid: 1 April 2010

https://projecteuclid.org/euclid.tjm/1270130249

Digital Object Identifier
doi:10.3836/tjm/1270130249

Mathematical Reviews number (MathSciNet)
MR1164184

Zentralblatt MATH identifier
0782.47036

#### Citation

deLAUBENFELS, Ralph. Holomorphic $C$-Existence Families. Tokyo J. Math. 15 (1992), no. 1, 17--38. doi:10.3836/tjm/1270130249. https://projecteuclid.org/euclid.tjm/1270130249