Differential and Integral Equations

A Stieltjes type convolution for integrated semigroups of bounded strong variation and $L_p$-solutions to the abstract Cauchy problem

Horst R. Thieme and Hauke Vosseler

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Abstract

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.

Article information

Source
Differential Integral Equations, Volume 15, Number 10 (2002), 1171-1218.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060751

Mathematical Reviews number (MathSciNet)
MR1919768

Zentralblatt MATH identifier
1041.47029

Subjects
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]

Citation

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


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