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Harmonic analysis on $S U (n, n) / S L (n, ℂ) \times ℝ_{+}$ .

Andersen, Nils Byrial; Unterberger, Jérémie M. — 2000

Journal of Lie Theory

An application of shift operators to ordered symmetric spaces

Nils Byrial Andersen; Jérémie M. Unterberger — 2002

Annales de l’institut Fourier

We study the action of elementary shift operators on spherical functions on ordered symmetric spaces $ℳ_{m, n}$ of Cayley type, where $m \in ℕ$ denotes the multiplicity of the short roots and $n \in ℕ$ the rank of the symmetric space. For $m$ even we apply this to prove a Paley-Wiener theorem for the spherical Laplace transform defined on $ℳ_{m, n}$ by a reduction to the rank 1 case. Finally we generalize our notions and results to $B C_{n}$ type root systems.

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Harmonic analysis on S U ( n , n ) / S L ( n , ℂ ) × ℝ + .

An application of shift operators to ordered symmetric spaces

Harmonic analysis on $S U (n, n) / S L (n, ℂ) \times ℝ_{+}$ .