Differential and Integral Equations
- Differential Integral Equations
- Volume 15, Number 10 (2002), 1171-1218.
A Stieltjes type convolution for integrated semigroups of bounded strong variation and $L_p$-solutions to the abstract Cauchy problem
A convolution of Stieltjes type is introduced for operator families of bounded strong variation and vector valued $L_1$-functions. Using this tool, perturbation theorems for integrated semigroups of bounded strong variation are derived, and improved results on $L_p$-solutions to the inhomogeneous Cauchy problem are obtained.
Differential Integral Equations, Volume 15, Number 10 (2002), 1171-1218.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47D62: Integrated semigroups
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 45N05: Abstract integral equations, integral equations in abstract spaces 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
Thieme, Horst R.; Vosseler, Hauke. A Stieltjes type convolution for integrated semigroups of bounded strong variation and $L_p$-solutions to the abstract Cauchy problem. Differential Integral Equations 15 (2002), no. 10, 1171--1218. https://projecteuclid.org/euclid.die/1356060751