C0-semigroup
Sign in to saveIn mathematical analysis, a '''C0-semigroup, also known as a strongly continuous one-parameter semigroup''', is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly continuous semigroups provide solutions of linear constant coefficient ordinary differential equations in Banach spaces. Such differential equations in Banach spaces arise from e.g. delay differential equations and partial differential equations.
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Article
21 sectionsContents
- Formal definition
- Infinitesimal generator
- Uniformly continuous semigroup
- Examples
- Multiplication semigroup
- Translation semigroup
- Abstract Cauchy problems
- Generation theorems
- Special classes of semigroups
- Uniformly continuous semigroups
- Analytic semigroups
- Contraction semigroups
- Differentiable semigroups
- Compact semigroups
- Norm continuous semigroups
- Stability
- Exponential stability
- Strong stability
- See also
- Notes
- References
In mathematical analysis, a '''C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly continuous semigroups provide solutions of linear constant coefficient ordinary differential equations in Banach spaces. Such differential equations in Banach spaces arise from e.g. delay differential equations and partial differential equations.
Formally, a strongly continuous semigroup is a representation of the semigroup (R'+, +) on some Banach space X that is continuous in the strong operator topology.