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Lemma 4.3 Assume • T(0) = Idx; • T(t +s) = T(t)T(s) (t, s 2 0); • Vx€ X :xH T(t)x is continuous in 0. Then T is a Co-semigroup.

Lemma 4.3 Assume • T(0) = Idx; • T(t +s) = T(t)T(s) (t, s 2 0); • Vx€ X :xH T(t)x is continuous in 0. Then T is a Co-semigroup.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove lemma 4.3 in the given picture

Lemma 4.3 Assume • T(0) = Idx; • T(t + s) = T(t)T(s) (t, s 2 0); • Vr€ X :rH T(t)x is continuous in 0. Then T is a Co-semigroup.
Transcribed Image Text:Lemma 4.3 Assume • T(0) = Idx; • T(t + s) = T(t)T(s) (t, s 2 0); • Vr€ X :rH T(t)x is continuous in 0. Then T is a Co-semigroup.
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