A note on a formula for the fractional powers of infinitesimal generators of semigroups

ArticleOriginal scientific text

Title

Authors ¹, ¹

Departament de Matemàtica Aplicada, Universitat de València, 46100 Burjassot, València, Spain

If -A is the generator of an equibounded

C_{0}

-semigroup and 0 < Re α < m (m integer), its fractional power

A^{α}

can be described in terms of the semigroup, through a formula that is only valid if a certain function

K_{α, m}

is nonzero. This paper is devoted to the study of the zeros of

K_{α, m}

.

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