Compactification via the Ground State
Identifieur interne : 001788 ( Main/Exploration ); précédent : 001787; suivant : 001789Compactification via the Ground State
Auteurs : Yves Guivarc [France] ; Lizhen Ji [États-Unis] ; J. C. Taylor [Canada]Source :
- Progress in Mathematics ; 1998.
Abstract
Abstract: The K-invariant probability m on F = G/P represents, by means of the square root of the Poisson kernel, a unique solution of the equation Lu + λ 0u = 0 with u(o) = 1. It is the spherical function Φ defined by $$\Phi \left( {g \cdot o} \right) = \int {_K{e^{ - \rho \left( {H\left( {{g^{ - 1}}k} \right)} \right)}}} dk = \int {_\mathcal{F}{P^{1/2}}\left( {x,b} \right)dm\left( b \right),} $$ where x = g · o ∈ X, b = kP, and $$P\left( {x,b} \right) = {e^{ - 2\rho \left( {H\left( {{g^{ - 1}}k} \right)} \right)}}$$ is the Poisson kernel on X (see §7.21 and § 8.27). It plays a basic role in harmonic analysis on semisimple groups, for example it dominates all the spherical functions associated with the unitary principal series, and is called the Harish-Chandra spherical function (see [G1]). It arose earlier in Chapter VII when determining the limit functions for the Martin compactification at the bottom of the positive spectrum.
Url:
DOI: 10.1007/978-1-4612-2452-5_10
Affiliations:
- Canada, France, États-Unis
- Michigan, Québec, Région Bretagne
- Montréal, Rennes
- Université McGill, Université de Rennes 1
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C." last="Taylor">J. C. Taylor</name><affiliation wicri:level="4"><country xml:lang="fr">Canada</country><wicri:regionArea>Department of Mathematics and Statistics, McGill University, Quebec, Montreal</wicri:regionArea><placeName><settlement type="city">Montréal</settlement><region type="state">Québec</region><settlement type="city">Montréal</settlement></placeName><orgName type="university">Université McGill</orgName></affiliation></author></analytic><monogr></monogr><series><title level="s">Progress in Mathematics</title><imprint><date>1998</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The K-invariant probability m on F = G/P represents, by means of the square root of the Poisson kernel, a unique solution of the equation Lu + λ 0u = 0 with u(o) = 1. It is the spherical function Φ defined by $$\Phi \left( {g \cdot o} \right) = \int {_K{e^{ - \rho \left( {H\left( {{g^{ - 1}}k} \right)} \right)}}} dk = \int {_\mathcal{F}{P^{1/2}}\left( {x,b} \right)dm\left( b \right),} $$ where x = g · o ∈ X, b = kP, and $$P\left( {x,b} \right) = {e^{ - 2\rho \left( {H\left( {{g^{ - 1}}k} \right)} \right)}}$$ is the Poisson kernel on X (see §7.21 and § 8.27). It plays a basic role in harmonic analysis on semisimple groups, for example it dominates all the spherical functions associated with the unitary principal series, and is called the Harish-Chandra spherical function (see [G1]). It arose earlier in Chapter VII when determining the limit functions for the Martin compactification at the bottom of the positive spectrum.</div></front></TEI><affiliations><list><country><li>Canada</li><li>France</li><li>États-Unis</li></country><region><li>Michigan</li><li>Québec</li><li>Région Bretagne</li></region><settlement><li>Montréal</li><li>Rennes</li></settlement><orgName><li>Université McGill</li><li>Université de Rennes 1</li></orgName></list><tree><country name="France"><region name="Région Bretagne"><name sortKey="Guivarc, Yves" sort="Guivarc, Yves" uniqKey="Guivarc Y" first="Yves" last="Guivarc">Yves Guivarc</name></region></country><country name="États-Unis"><region name="Michigan"><name sortKey="Ji, Lizhen" sort="Ji, Lizhen" uniqKey="Ji L" first="Lizhen" last="Ji">Lizhen Ji</name></region></country><country name="Canada"><region name="Québec"><name sortKey="Taylor, J C" sort="Taylor, J C" uniqKey="Taylor J" first="J. C." last="Taylor">J. C. Taylor</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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