Anker, JeanPhilippe
Overview
Works:  23 works in 75 publications in 2 languages and 1,663 library holdings 

Roles:  Author, Editor 
Classifications:  QA252.3, 512.55 
Publication Timeline
.
Most widely held works by
JeanPhilippe Anker
Lie theory : unitary representations and compactifications of symmetric spaces by
JeanPhilippe Anker(
Book
)
21 editions published in 2005 in English and Undetermined and held by 274 WorldCat member libraries worldwide
"Unitary Representations and Compactifications of Symmetric Spaces, a selfcontained work by A. Borel, L. Ji, and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications: and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles."Résumé de l'éditeur
21 editions published in 2005 in English and Undetermined and held by 274 WorldCat member libraries worldwide
"Unitary Representations and Compactifications of Symmetric Spaces, a selfcontained work by A. Borel, L. Ji, and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications: and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles."Résumé de l'éditeur
Lie theory : Lie algebras and representations by
Jens Carsten Jantzen(
Book
)
10 editions published between 2003 and 2004 in English and held by 260 WorldCat member libraries worldwide
"Ideal for graduate students and researchers, Lie Theory provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics."Jacket
10 editions published between 2003 and 2004 in English and held by 260 WorldCat member libraries worldwide
"Ideal for graduate students and researchers, Lie Theory provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics."Jacket
Lie theory : harmonic analysis on symmetric spaces, general Plancherel theorems by
JeanPhilippe Anker(
Book
)
18 editions published in 2005 in English and held by 253 WorldCat member libraries worldwide
"Harmonic Analysis on Symmetric Spaces  General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces." "Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, and possibly even mathematical cosmology, Harmonic Analysis on Symmetric Spaces  General Plancherel Theorems provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required."Jacket
18 editions published in 2005 in English and held by 253 WorldCat member libraries worldwide
"Harmonic Analysis on Symmetric Spaces  General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces." "Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, and possibly even mathematical cosmology, Harmonic Analysis on Symmetric Spaces  General Plancherel Theorems provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required."Jacket
Aspects de la pinduction en analyse harmonique by
JeanPhilippe Anker(
Book
)
4 editions published in 1982 in French and Undetermined and held by 21 WorldCat member libraries worldwide
4 editions published in 1982 in French and Undetermined and held by 21 WorldCat member libraries worldwide
Théorèmes ergodiques pour les actions de groupes(
Book
)
2 editions published in 2010 in French and held by 14 WorldCat member libraries worldwide
2 editions published in 2010 in French and held by 14 WorldCat member libraries worldwide
Lie algebras and representations by
Jens Carsten Jantzen(
Book
)
1 edition published in 2004 in English and held by 10 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 10 WorldCat member libraries worldwide
Harmonic analysis on symmetric spaces  general Plancherel theorems(
Book
)
1 edition published in 2005 in English and held by 9 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 9 WorldCat member libraries worldwide
Estimations globales du noyau de la chaleur by
Patrick Jacques Ostellari(
)
2 editions published in 2003 in French and held by 2 WorldCat member libraries worldwide
This thesis deals with sharp heat kernel estimates in two related settings. We consider first noncompact Riemannian symmetric spaces X = G/K, and obtain in this case the same upper and lower bound for the heat kernel associated with the LaplaceBeltrami operator L. These bounds are global in space and time. We consider next the class of subLaplacians on a semisimple Lie group G which induce L on the associated symmetric space X = G/K. These subLaplacians share properties with L: they have the same L^2 spectral gap, the associated CarnotCarathéodory distances are all comparable with the Riemannian metric on X and, most of all, their heat kernels are all comparable (for large time) with the heat kernel on X. This yields sharp heat kernel bounds and, consequently, optimal Green function estimates
2 editions published in 2003 in French and held by 2 WorldCat member libraries worldwide
This thesis deals with sharp heat kernel estimates in two related settings. We consider first noncompact Riemannian symmetric spaces X = G/K, and obtain in this case the same upper and lower bound for the heat kernel associated with the LaplaceBeltrami operator L. These bounds are global in space and time. We consider next the class of subLaplacians on a semisimple Lie group G which induce L on the associated symmetric space X = G/K. These subLaplacians share properties with L: they have the same L^2 spectral gap, the associated CarnotCarathéodory distances are all comparable with the Riemannian metric on X and, most of all, their heat kernels are all comparable (for large time) with the heat kernel on X. This yields sharp heat kernel bounds and, consequently, optimal Green function estimates
Analyse harmonique des formes différentielles sur l'espace hyperbolique réel by
Emmanuel Pedon(
Book
)
1 edition published in 1997 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1997 in English and held by 2 WorldCat member libraries worldwide
Spherical analysis on harmonic on groups by
JeanPhilippe Anker(
Book
)
2 editions published in 1994 in Undetermined and English and held by 2 WorldCat member libraries worldwide
2 editions published in 1994 in Undetermined and English and held by 2 WorldCat member libraries worldwide
Analyse harmonique et équation de Schrödinger associées au laplacien de Dunkl trigonométrique by
Fatma Ayadi Ben Said(
)
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
This thesis consists of three chapters. The first one is concerned with energy properties of the wave equation associated with the trigonometric Dunkl Laplacian. We establish the conservation of the total energy, the strict equipartition of energy under suitable assumptions and the asymptotic equipartition in the general case. These results were published in [8]. The second chapter, in collaboration with J.Ph. Anker and M. Sifi [6], shows that Opdam's functions in the rank one case satisfy a product formula. We then define and study a convolution structure related to Opdam's functions. In particular, we prove that this convolution fulfills a KunzeStein type phenomena. The last chapter deals with dispersive and Strichartz estimates for the linear Schrödinger equation associated with the one dimensional trigonometric Dunkl Laplacian [7]. We establish sharp estimates for the heat kernel in complex time, and therefore for the Schrödinger kernel. We then use these estimates together with tools from chapter 2 to deduce dispersive and Strichartz inequalities for the linear Schrödinger equation and apply them to wellposedness in the nonlinear case
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
This thesis consists of three chapters. The first one is concerned with energy properties of the wave equation associated with the trigonometric Dunkl Laplacian. We establish the conservation of the total energy, the strict equipartition of energy under suitable assumptions and the asymptotic equipartition in the general case. These results were published in [8]. The second chapter, in collaboration with J.Ph. Anker and M. Sifi [6], shows that Opdam's functions in the rank one case satisfy a product formula. We then define and study a convolution structure related to Opdam's functions. In particular, we prove that this convolution fulfills a KunzeStein type phenomena. The last chapter deals with dispersive and Strichartz estimates for the linear Schrödinger equation associated with the one dimensional trigonometric Dunkl Laplacian [7]. We establish sharp estimates for the heat kernel in complex time, and therefore for the Schrödinger kernel. We then use these estimates together with tools from chapter 2 to deduce dispersive and Strichartz inequalities for the linear Schrödinger equation and apply them to wellposedness in the nonlinear case
Lie theory(
Book
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Etude analytique et probabiliste de laplaciens associés à des systèmes de racines by
Bruno Schapira(
Book
)
1 edition published in 2006 in French and held by 1 WorldCat member library worldwide
Cette thèse porte sur une étude analytique et probabiliste des théories de HeckmanOpdam et des immeubles affines de type Ãr. On étudie aussi la frontière de Poisson des matrices triangulaires inversibles rationnelles. Un de nos principaux résultats est l'obtention de nouvelles estimations des fonctions hypergéométriques de HeckmanOpdam. Nos preuves sont relativement plus simples que dans le cas particulier des espaces symétriques G/K. Par exemple pour les estimations de base des fonctions sphériques, obtenues par HarishChandra, ou Gangolli et Varadarajan, ainsi que pour les estimations récentes de la fonction sphérique élémentaire o par Anker, Bougerol et Jeulin. Un des autres principaux résultats est l'estimation du noyau de la chaleur associé à un certain laplacien combinatoire sur un immeuble affine de type Ãr
1 edition published in 2006 in French and held by 1 WorldCat member library worldwide
Cette thèse porte sur une étude analytique et probabiliste des théories de HeckmanOpdam et des immeubles affines de type Ãr. On étudie aussi la frontière de Poisson des matrices triangulaires inversibles rationnelles. Un de nos principaux résultats est l'obtention de nouvelles estimations des fonctions hypergéométriques de HeckmanOpdam. Nos preuves sont relativement plus simples que dans le cas particulier des espaces symétriques G/K. Par exemple pour les estimations de base des fonctions sphériques, obtenues par HarishChandra, ou Gangolli et Varadarajan, ainsi que pour les estimations récentes de la fonction sphérique élémentaire o par Anker, Bougerol et Jeulin. Un des autres principaux résultats est l'estimation du noyau de la chaleur associé à un certain laplacien combinatoire sur un immeuble affine de type Ãr
Equations d'évolution sur certains groupes hyperboliques by
Alaa Jamal Eddine(
)
1 edition published in 2013 in French and held by 1 WorldCat member library worldwide
This thesis focuses on the study of evolution equations on certain hyperbolic groups, in particular, we study the heat equation, the Schrödinger equation and the modified wave equation first on homogeneous trees then on symmetric graphs. In the homogeneous trees case, we show that under a gauge invariance condition, we have global existence of solutions of the Schrödinger equation and scattering for arbitrary data in the space of square integrable functions without any restriction on the degree of the nonlinearity, in contrast to the euclidean and hyperbolic space cases. We then generalize this result on symmetric graphs of degree (k  1)(r  1) under the condition k < r . One of our main results on symmetric graphs is the estimate of the heat kernel associated to the combinatorial laplacian. Finally, we establish an explicit expression of solutions of the modified wave equation on symmetric graphs
1 edition published in 2013 in French and held by 1 WorldCat member library worldwide
This thesis focuses on the study of evolution equations on certain hyperbolic groups, in particular, we study the heat equation, the Schrödinger equation and the modified wave equation first on homogeneous trees then on symmetric graphs. In the homogeneous trees case, we show that under a gauge invariance condition, we have global existence of solutions of the Schrödinger equation and scattering for arbitrary data in the space of square integrable functions without any restriction on the degree of the nonlinearity, in contrast to the euclidean and hyperbolic space cases. We then generalize this result on symmetric graphs of degree (k  1)(r  1) under the condition k < r . One of our main results on symmetric graphs is the estimate of the heat kernel associated to the combinatorial laplacian. Finally, we establish an explicit expression of solutions of the modified wave equation on symmetric graphs
Lie Theory Unitary Representations and Compactifications of Symmetric Spaces. Progress in Mathematics, Volume 229(
)
1 edition published in 2005 in English and held by 0 WorldCat member libraries worldwide
Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a selfcontained work by A. Borel, L. Ji and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e. restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles. Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples and provides a good background for the second chapter, namely, the BorelJi authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Kobayashi examines the important subject of branching laws. Knowledge of basic representation theory of Lie groups and familiarity with semisimple Lie groups and symmetric spaces is required of the reader
1 edition published in 2005 in English and held by 0 WorldCat member libraries worldwide
Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a selfcontained work by A. Borel, L. Ji and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e. restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles. Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples and provides a good background for the second chapter, namely, the BorelJi authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Kobayashi examines the important subject of branching laws. Knowledge of basic representation theory of Lie groups and familiarity with semisimple Lie groups and symmetric spaces is required of the reader
Lie Theory Volume 230, Harmonic Analysis on Symmetric Spaces  General Plancherel Theorems by
JeanPhilippe Anker(
)
1 edition published in 2005 in English and held by 0 WorldCat member libraries worldwide
Suitable for both graduate students and researchers in semi simple Lie theory and neighboring fields, this work provides an examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics
1 edition published in 2005 in English and held by 0 WorldCat member libraries worldwide
Suitable for both graduate students and researchers in semi simple Lie theory and neighboring fields, this work provides an examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics
Lie Theory Harmonic Analysis on Symmetric SpacesGeneral Plancherel Theorems. Progress in Mathematics, Volume 230(
)
1 edition published in 2005 in English and held by 0 WorldCat member libraries worldwide
Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, selfcontained volumes, under the general title of Lie Theory, feature survey work and original results by wellestablished researchers in key areas of semisimple Lie theory. Harmonic Analysis on Symmetric Spaces  General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces. Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology, it provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required
1 edition published in 2005 in English and held by 0 WorldCat member libraries worldwide
Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, selfcontained volumes, under the general title of Lie Theory, feature survey work and original results by wellestablished researchers in key areas of semisimple Lie theory. Harmonic Analysis on Symmetric Spaces  General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces. Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology, it provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required
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