On Lie Semi-Groups
1960 ◽
Vol 12
◽
pp. 686-693
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Keyword(s):
Suppose we have a semi-group structure defined ona subset of real Euclidean n-space, En, by (p, q) → F (p, q) = poq. In this note we shall be concerned with a representation T(.) of π as a semi-group of bounded linear operators on a Banach space 𝒳. More particularly, we suppose that postulates P1, P2, P3, P5 and P6 of chapter 25 of (2) are satisfied so that, by Theorem 25.3.1 of that book, there is a continuous function, f(.), defined on π such that f((ρ + σ)a) = f(ρa)o f(σa) for a ∈ π, ρ,σ ≥ 0; that the representation is strongly continuous in a neighbourhood of the origin and that T(0) = I.
1978 ◽
Vol 30
(5)
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pp. 1045-1069
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Keyword(s):
1984 ◽
Vol 96
(3)
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pp. 483-493
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2016 ◽
Vol 160
(3)
◽
pp. 413-421
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1969 ◽
Vol 16
(3)
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pp. 227-232
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Keyword(s):
1988 ◽
Vol 31
(1)
◽
pp. 127-144
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Keyword(s):
1986 ◽
Vol 29
(1)
◽
pp. 15-21
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1969 ◽
Vol 21
◽
pp. 592-594
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1974 ◽
Vol 26
(6)
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pp. 1430-1441
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Keyword(s):