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- W4310682247 abstract "The description of the Paley–Wiener space for compactly supported smooth functions $$C^infty _c(G)$$ on a semi-simple Lie group G involves certain intertwining conditions that are difficult to handle. In the present paper, we make them completely explicit for $$G=textbf{SL}(2,mathbb {R})^d$$ ( $$din mathbb {N}$$ ) and $$G=textbf{SL}(2,mathbb {C})$$ . Our results are based on a defining criterion for the Paley–Wiener space, valid for general groups of real rank one, that we derive from Delorme’s proof of the Paley–Wiener theorem. In a forthcoming paper, we will show how these results can be used to study solvability of invariant differential operators between sections of homogeneous vector bundles over the corresponding symmetric spaces." @default.
- W4310682247 created "2022-12-15" @default.
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- W4310682247 date "2022-12-05" @default.
- W4310682247 modified "2023-10-16" @default.
- W4310682247 title "Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces" @default.
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- W4310682247 doi "https://doi.org/10.1007/s10455-022-09882-w" @default.
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