Tame algebra estimates for product and flag kernels on graded Lie groups
Amelia Stokolosa

TL;DR
This paper establishes tame algebra estimates for product and flag kernels on graded Lie groups, providing a new Banach-algebraic proof of their inversion theorem, which is important for nonlinear PDE analysis.
Contribution
It introduces tame algebra estimates for these kernels on graded Lie groups and offers a novel Banach-algebraic proof of their inversion theorem.
Findings
Proved tame algebra estimates for product and flag kernels.
Derived a new Banach-algebraic inversion theorem.
Enhanced tools for nonlinear PDE analysis on graded Lie groups.
Abstract
We prove that product kernels and flag kernels on a direct product of graded Lie groups satisfy so-called \emph{tame algebra estimates}. Tame algebra estimates are central to the study of nonlinear partial differential equations via, for instance, the Nash-Moser inverse function theorem. In addition, the special structure of these estimates generates a new Banach-algebraic proof of an inversion theorem for product kernels and flag kernels.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Physics Problems · Advanced Operator Algebra Research
