Data di Pubblicazione:
2019
Citazione:
Paley–Wiener Theorems on the Siegel Upper Half-Space / N. Arcozzi, A. Monguzzi, M.M. Peloso, M. Salvatori. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - (2019). [Epub ahead of print]
Abstract:
In this paper we study spaces of holomorphic functions on the Siegel upper half-space
U and prove Paley–Wiener type theorems for such spaces. The boundary of U can
be identified with the Heisenberg group Hn. Using the group Fourier transform on
Hn, Ogden and Vagi (Adv Math 33(1):31–92, 1979) proved a Paley–Wiener theorem
for the Hardy space H2(U). We consider a scale of Hilbert spaces on 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 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 D˙ is the unique Hilbert space norm that is invariant under the action of the
group of automorphisms of U
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Siegel upper half-space; Holomorphic function spaces; Reproducing kernel Hilbert space; Drury–Arveson; Dirichlet; Hardy; Bergman spaces;
Elenco autori:
N. Arcozzi, A. Monguzzi, M.M. Peloso, M. Salvatori
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