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Analytic continuation for Flensted-Jensen Representations.

Gestur Olafsson; Bent Orsted — 1992

Manuscripta mathematica

L...-versions of the Howe correspondence I.

Genkai Zhang; Bent Orsted — 1997

Mathematica Scandinavica

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

Khalid Koufany; Bent Ørsted — 1996

Annales de l'institut Fourier

For the scalar holomorphic discrete series representations of $SU (2, 2)$ and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside $SU (2, 2)$ . We construct a Cayley transform between the Ol’shanskiĭ semigroup having $U (1, 1)$ as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for $SU (2, 2)$ . This allows calculating the composition series in terms of harmonic analysis on $U (1, 1)$ . In particular we show that the Ol’shanskiĭ Hardy space for $U (1, 1)$ is different...

A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform

Bent Ørsted; Jorge Vargas — 2007

Annales de l’institut Fourier

In this note, we generalize the results in our previous paper on the Casimir operator and Berezin transform, by showing the $(L^{2}, L^{2})$ -continuity of a generalized Berezin transform associated with a branching problem for a class of unitary representations defined by invariant elliptic operators; we also show, that under suitable general conditions, this generalized Berezin transform is $(L^{p}, L^{p})$ -continuous for $1 \leq p \leq \infty .$

Conformal indices of riemannian manifolds

Thomas P. Branson; Bent Ørsted — 1986

Compositio Mathematica

Conformally invariant trilinear forms on the sphere

Jean-Louis Clerc; Bent Ørsted — 2011

Annales de l’institut Fourier

To each complex number $λ$ is associated a representation $π_{λ}$ of the conformal group $S O_{0} (1, n)$ on $𝒞^{\infty} (S^{n - 1})$ (spherical principal series). For three values $λ_{1}, λ_{2}, λ_{3}$ , we construct a trilinear form on $𝒞^{\infty} (S^{n - 1}) \times 𝒞^{\infty} (S^{n - 1}) \times 𝒞^{\infty} (S^{n - 1})$ , which is invariant by $π_{λ_{1}} \otimes π_{λ_{2}} \otimes π_{λ_{3}}$ . The trilinear form, first defined for $(λ_{1}, λ_{2}, λ_{3})$ in an open set of $ℂ^{3}$ is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms.

Conal Heisenberg algebras and associated Hilbert spaces.

J. Hilgert; K.-H. Neeb; Bent Orsted — 1996

Journal für die reine und angewandte Mathematik

Relative discrete series of line bundles over bounded symmetric domains

Anthony H. Dooley; Bent Ørsted; Genkai Zhang — 1996

Annales de l'institut Fourier

We study the relative discrete series of the $L^{2}$ -space of the sections of a line bundle over a bounded symmetric domain. We prove that all the discrete series appear as irreducible submodules of the tensor product of a holomorphic discrete series with a finite dimensional representation.

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