Journal of Lie Theory

no. 2
A Paley-Wiener Theorem for the Bessel Laplace Transform,<br/> I: the case SU(n,n)/SL(n,C) x R*+
Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 253-271
\def\C{{\Bbb C}} \def\R{{\Bbb R}} \def\q{{\frak q}} Let $\q$ be the tangent space to the noncompact causal symmetric space $$SU(n,n)/SL(n,\C)\times \R^*_+$$ at the origin. In this paper we give an explicit formula for the Bessel functions on $\q$. We use this result to prove a Paley-Wiener theorem for the Bessel Laplace transform on $\q$. Further, a flat analogue of the Abel transform is defined and inverted.
DOI: 10.5802/jolt.493
Classification: 43A85, 43A32, 33C80
Keywords: Non-compactly causal symmetric spaces, multivariable Bessel function, Paley-Wiener theorem, Abel transform 
@article{JOLT_2008_18_2_a0,
     author = {S. Ben Sa{\"\i}d},
     title = {A {Paley-Wiener} {Theorem} for the {Bessel} {Laplace} {Transform,<br/>
I:} the case {SU(n,n)/SL(n,C)} x {R*\protect\textsubscript{+}}},
     journal = {Journal of Lie Theory},
     pages = {253--271},
     year = {2008},
     volume = {18},
     number = {2},
     doi = {10.5802/jolt.493},
     zbl = {1146.43007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.493/}
}
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I: the case SU(n,n)/SL(n,C) x R*+
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S. Ben Saïd. A Paley-Wiener Theorem for the Bessel Laplace Transform,

I: the case SU(n,n)/SL(n,C) x R*+. Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 253-271. doi: 10.5802/jolt.493

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