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- W2124014738 abstract "Let $G$ be an exponential solvable Lie group, and $pi$ be an irreducible unitary representation of $G$. Then by induction from a unitary character of a connected subgroup, $pi$ is realized in an $L^2$-space of functions on a homogeneous space. We are concerned with $C^infty$vectors of $pi$ from a viewpoint of rapidly decreasing properties. We show that the subspace $mathscr{PE}$ consisting of vectors with a certain property of rapidly decreasing at infinity can be embedded as the space of the $C^infty$vectors in an extension of $pi$ to an exponential group including $G$. Using the space $mathscr{PE}$, we also give a description of the space $mathscr{APE}$ related to Fourier transforms of $L^1$-functions on $G$. We next obtain an explicit description of $C^infty$vectors for a special case. Furthermore, we consider a space of functions on $G$ with a similar rapidly decreasing property and show that it is the space of the $C^infty$vectors of an irreducible representation of a certain exponential solvable Lie group acting on $L^2(G)$." @default.
- W2124014738 created "2016-06-24" @default.
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- W2124014738 date "2007-10-01" @default.
- W2124014738 modified "2023-09-25" @default.
- W2124014738 title "$C^{infty}$-vectors of irreducible representations of exponential solvable Lie groups" @default.
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- W2124014738 doi "https://doi.org/10.2969/jmsj/05941081" @default.
- W2124014738 hasPublicationYear "2007" @default.
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