On multidimensional Bochner-Phillips functional calculus
A.R. Mirotin
TL;DR
This paper develops a multidimensional Bochner-Phillips functional calculus for semigroup generators, providing conditions for holomorphy and establishing moment inequalities in the one-dimensional case, advancing the mathematical understanding of operator functions.
Contribution
It introduces a multidimensional functional calculus based on Bernstein functions, with new conditions for semigroup holomorphy and moment inequalities in one dimension.
Findings
Established conditions for holomorphy of semigroups generated by these operators.
Developed a multidimensional functional calculus framework.
Proved moment inequalities for one-dimensional cases.
Abstract
The functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the condition for holomorphy of semigroups, generated by operators which arisen in the calculus is given, and in the one-dimensional case the moment inequality for such operators is proved.
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Taxonomy
Topicsadvanced mathematical theories · Nonlinear Differential Equations Analysis · Differential Equations and Boundary Problems