Fréchet Differentiability of Parameter-Dependent Analytic Semigroups
Copyright policy )Fréchet Differentiability of Parameter-Dependent Analytic Semigroups
The authors study dependence on a vector-valued parameter \(q\) of a collection of analytic semigroups \(\{T(t;q), t\geq 0\}\). The analyticity of the map \(q\mapsto T(t;q)\) in the uniform operator topology is established and, moreover, the Fréchet derivative of \(T(t;q)\) with respect to \(q\) is given by a norm-convergent contour integral.
- Bowling Green State University United States
- University System of Ohio United States
Gelfand triples, resolvent perturbation, One-parameter semigroups and linear evolution equations, Derivatives of functions in infinite-dimensional spaces, Applied Mathematics, analytic semigroups, inverse Laplace transform, collection of analytic semigroups, dependence on a vector-valued parameter, norm-convergent contour integral, Fréchet derivative, Fréchet differentiability, parameterized evolution equations, Analysis, abstract elliptic operators
Gelfand triples, resolvent perturbation, One-parameter semigroups and linear evolution equations, Derivatives of functions in infinite-dimensional spaces, Applied Mathematics, analytic semigroups, inverse Laplace transform, collection of analytic semigroups, dependence on a vector-valued parameter, norm-convergent contour integral, Fréchet derivative, Fréchet differentiability, parameterized evolution equations, Analysis, abstract elliptic operators
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