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- W2891083212 abstract "Let $mathbb{G}$ be a higher-rank connected semisimple Lie group with finite center and without compact factors. In any unitary representation $(pi, mathcal{H})$ of $mathbb{G}$ without non-trivial $mathbb{G}$-fixed vectors, we study the twisted cohomological equation $(X+m)f=g$, where $minmathbb{R}$ and $X$ is in a $mathbb{R}$-split Cartan subalgebra of $text{Lie}(mathbb{G})$. We characterize the obstructions to solving the cohomological equation, construct smooth solutions of the cohomological equation and obtain tame Sobolev estimates for $f$. We also study common solution to (the infinitesimal version of) the twisted cocycle equation $(X+m)g_1=(mathfrak{v}+m_1)g_2$, where $mathfrak{v}$ is nilpotent or in a $mathbb{R}$-split Cartan subalgebra, $m,m_1inmathbb{R}$. This is the first paper studying general twisted equations. Compared to former papers, a new technique in representation theory is developed by Mackey theory and Mellin transform." @default.
- W2891083212 created "2018-09-27" @default.
- W2891083212 creator A5013482173 @default.
- W2891083212 date "2018-09-12" @default.
- W2891083212 modified "2023-09-27" @default.
- W2891083212 title "The twisted cohomological equation over the partially hyperbolic flow" @default.
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- W2891083212 hasPublicationYear "2018" @default.
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