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Zbl 0738.47037
Thieme, Horst R.
"Integrated semigroups" and integrated solutions to abstract Cauchy problems. (English)
[J] J. Math. Anal. Appl. 152, No.2, 416-447 (1990). ISSN 0022-247X

Summary: Concepts which have been developed in the theory of weakly $\sp*$ continuous semigroups on dual Banach spaces are extended to ``integrated semigroups''. The relation to integrated solutions of homogeneous and inhomogeneous abstract Cauchy problems is established. The results are illustrated for the wave equation in $L\sb 2(\bbfR\sp m)$.

MSC 2000:: *47D06 One-parameter semigroups and linear evolution equations

Keywords: weakly* continuous semigroups on dual Banach spaces; integrated semigroups; homogeneous and inhomogeneous abstract Cauchy problems; wave equation

Cited in: Zbl 1052.47040 Zbl 0903.47025

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Zentralblatt MATH Berlin [Germany]