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)
In operator theory, a bounded operator ''T'': ''X'' → ''Y'' between normed vector spaces ''X'' and ''Y'' is said to be a contraction if its operator norm , , ''T'' , , ≤ 1. This notion is a special case of the concept of a contractio ...
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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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