A Paley-Wiener theorem for the bessel-laplace transform, I: The case SU(n,n)/SL(n,ℂ) x ℝ+*

Salem Ben Saïd

A Paley-Wiener theorem for the bessel-laplace transform, I: The case SU(n,n)/SL(n,ℂ) x ℝ₊*

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Abstract

Let q be the tangent space to the noncompact causal symmetric space SU(n,n)/SL(n,ℂ) x 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.

Original language	English
Pages (from-to)	253-271
Number of pages	19
Journal	Journal of Lie Theory
Volume	18
Issue number	2
Publication status	Published - 2008
Externally published	Yes

Keywords

Abel transform
Multivariable bessel function
Non-compactly causal symmetric spaces
Paley-Wiener theorem

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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keywords = "Abel transform, Multivariable bessel function, Non-compactly causal symmetric spaces, Paley-Wiener theorem",

author = "{Ben Sa{\"i}d}, Salem",

year = "2008",

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AB - Let q be the tangent space to the noncompact causal symmetric space SU(n,n)/SL(n,ℂ) x 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.

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KW - Multivariable bessel function

KW - Non-compactly causal symmetric spaces

KW - Paley-Wiener theorem

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A Paley-Wiener theorem for the bessel-laplace transform, I: The case SU(n,n)/SL(n,ℂ) x ℝ₊*

Abstract

Keywords

ASJC Scopus subject areas

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