Functional calculus for generators of analytic semigroups of operators

O. V. Lopushansky, S. V. Sharyn


We construct a functional calculus for generators of one-parameter bounded analytic semigroups of operators on a Banach space. The calculus symbol class consist of the Laplace image of the convolution algebra $\cal S'_+$ of tempered distributions with supports in $[0, \infty)$. Domain of constructed calculus is dense in the Banach space.

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