On the connections of Hille-Phillips functional calculus with Bochner-Phillips functional calculus
A. R. Mirotin
TL;DR
This paper explores the relationship between Hille-Phillips and Bochner-Phillips functional calculi for semigroup generators, establishing rules and providing examples to deepen understanding of their connection.
Contribution
It demonstrates the multiplication and composition rules linking the two calculi and offers illustrative examples, advancing the theoretical framework of operator calculus.
Findings
Established multiplication rule connecting the calculi
Proved composition rule for the calculi
Provided examples illustrating the calculus connections
Abstract
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is considered. Connections of this calculus to Bochner-Phillips functional calculus are indicated. In particular, the multiplication rule and the composition rule are proved. Several examples are given.
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Taxonomy
TopicsMatrix Theory and Algorithms · Functional Equations Stability Results · Fractional Differential Equations Solutions