Stieltjes vectors and cosine functions generators

Ioana Cioranescu; Urlich Neumann

Displaying similar documents to “Stieltjes vectors and cosine functions generators”

Strongly continuous integrated C-cosine operator functions

Shen Wang, Zhen Huang (1997)

Studia Mathematica

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We extend some recent results for regularized semigroups to strongly continuous n-times integrated C-cosine operator functions. Several equivalent conditions for the existence and uniqueness of solutions of (ACP $_{2}$ ) are also presented.

On analytic semigroups and cosine functions in Banach spaces

V. Keyantuo, P. Vieten (1998)

Studia Mathematica

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If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform. ...