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Some Remarks on Talenti's Semigroup

Published online by Cambridge University Press:  20 November 2018

A. Chrysovergis
A. Chrysovergis*
Affiliation:
Sir George Williams University, Montreal, Quebec
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Let X be a Banach space. Consider the family I(α) of linear continuous operators from X into itself, depending on the parameter α ≥ 0. Suppose that I(α1+α2)=I(α1)I(α2)∀α1, α2 ≥ 0 and I(0)=I (semigroupal property). Such a semigroup is said to be strongly continuous for α > 0, if limh→0I(α+h)x =I(α)x, ∀x ∊ X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 147 - 150
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Talenti, G., Sul Problema di Cauchy Per Le Equazioni A Derivate Parziali, Ann. Mat. Pura Appl. Vol. LXVII, (1965), 365-394.Google Scholar
2. Hille, Einar and Phillips, Ralph S., Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ., v. 31.Google Scholar