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- W2765228112 abstract "In this paper we study spaces of holomorphic functions on the Siegel upper half-space $${mathcal U}$$ and prove Paley–Wiener type theorems for such spaces. The boundary of $${mathcal U}$$ can be identified with the Heisenberg group $${mathbb H}_n$$ . Using the group Fourier transform on $${mathbb H}_n$$ , Ogden and Vagi (Adv Math 33(1):31–92, 1979) proved a Paley–Wiener theorem for the Hardy space $$H^2({mathcal U})$$ . We consider a scale of Hilbert spaces on $${mathcal U}$$ that includes the Hardy space, the weighted Bergman spaces, the weighted Dirichlet spaces, and in particular the Drury–Arveson space, and the Dirichlet space $${mathcal D}$$ . For each of these spaces, we prove a Paley–Wiener theorem, some structure theorems, and provide some applications. In particular we prove that the norm of the Dirichlet space modulo constants $$dot{{mathcal D}}$$ is the unique Hilbert space norm that is invariant under the action of the group of automorphisms of $${mathcal U}$$ ." @default.
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- W2765228112 date "2019-02-14" @default.
- W2765228112 modified "2023-10-15" @default.
- W2765228112 title "Paley–Wiener Theorems on the Siegel Upper Half-Space" @default.
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- W2765228112 doi "https://doi.org/10.1007/s00041-019-09662-4" @default.
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