The unbounded extension of Hille-Phillips functional calculus
A. R. Mirotin
TL;DR
This paper extends the Hille-Phillips functional calculus to include unbounded operators, explores its relation to Bochner-Phillips calculus, and provides several illustrative examples.
Contribution
It introduces an unbounded extension of the Hille-Phillips calculus and discusses its connections to Bochner-Phillips calculus, with practical examples.
Findings
Extension to unbounded operators achieved
Connections to Bochner-Phillips calculus established
Multiple examples illustrating the extension
Abstract
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is given. Connections of this calculus to Bochner-Phillips functional calculus are indicated, and several examples are considered.
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Taxonomy
TopicsFunctional Equations Stability Results · Mathematical and Theoretical Analysis · Fixed Point Theorems Analysis