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strongly continuous semigroup

   Also found in: Wikipedia 0.01 sec.
strongly continuous semigroup [¦strȯŋ·lē kən¦tin·yə·wəs ′sem·i‚grüp]
(mathematics)
A semigroup of bounded linear operators on a Banach spaceB, together with a bijective mappingTfrom the positive real numbers onto the semigroup, such thatT(0) is the identity operator onB, T(s+t) =T(s)T(t) for any two positive numberssandtand, for each elementxofB, T(t)xis a continuous function oft.


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Among his topics are strongly continuous semigroups, compatible and regular systems, stabilization and detection, and time discrete systems.
After a short introduction to the theory of strongly continuous semigroups on linear operators on Banach spaces, the authors introduce abstract delay equations on a Banach space X and discuss examples.
 
 
 
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