Volume growth, temperedness and integrability of matrix coefficients on a real spherical space

Friedrich Knop; Bernhard Krötz; Eitan Sayag; Henrik Schlichtkrull

doi:10.1016/j.jfa.2016.04.001

Volume growth, temperedness and integrability of matrix coefficients on a real spherical space

Friedrich Knop, Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We apply the local structure theorem from [13] and the polar decomposition of [12] to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure L^p-integrability of matrix coefficients on Z.

Original language	American English
Pages (from-to)	12-36
Number of pages	25
Journal	Journal of Functional Analysis
Volume	271
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2016.04.001
State	Published - 1 Jul 2016

Keywords

Harmonic analysis on reductive groups
Real spherical spaces

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/j.jfa.2016.04.001

Cite this

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title = "Volume growth, temperedness and integrability of matrix coefficients on a real spherical space",

abstract = "We apply the local structure theorem from [13] and the polar decomposition of [12] to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure Lp-integrability of matrix coefficients on Z.",

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AU - Krötz, Bernhard

AU - Sayag, Eitan

AU - Schlichtkrull, Henrik

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N2 - We apply the local structure theorem from [13] and the polar decomposition of [12] to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure Lp-integrability of matrix coefficients on Z.

AB - We apply the local structure theorem from [13] and the polar decomposition of [12] to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure Lp-integrability of matrix coefficients on Z.

KW - Harmonic analysis on reductive groups

KW - Real spherical spaces

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JO - Journal of Functional Analysis

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IS - 1

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Volume growth, temperedness and integrability of matrix coefficients on a real spherical space

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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