In
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
, a
''C''0-semigroup Γ(''t''), ''t'' ≥ 0, is called a quasicontraction semigroup if there is a constant ''ω'' such that , , Γ(''t''), , ≤ exp(''ωt'') for all ''t'' ≥ 0. Γ(''t'') is called a contraction semigroup if , , Γ(''t''), , ≤ 1 for all ''t'' ≥ 0.
See also
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Contraction (operator theory)
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Hille-Yosida theorem
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Lumer-Phillips theorem
References
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Functional analysis
Semigroup theory
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