Anker, JeanPhilippe
Overview
Works:  24 works in 68 publications in 2 languages and 1,425 library holdings 

Roles:  Author, Editor, Thesis advisor, Opponent 
Classifications:  QA649, 516.362 
Publication Timeline
.
Most widely held works by
JeanPhilippe Anker
Lie theory : unitary representations and compactifications of symmetric spaces by
JeanPhilippe Anker(
Book
)
18 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
18 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
Lie theory : harmonic analysis on symmetric spaces, general Plancherel theorems by
JeanPhilippe Anker(
Book
)
19 editions published in 2005 in English and held by 254 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
19 editions published in 2005 in English and held by 254 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
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 15 WorldCat member libraries worldwide
2 editions published in 2010 in French and held by 15 WorldCat member libraries worldwide
Lie algebras and representations by
Jens Carsten Jantzen(
Book
)
1 edition published in 2004 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 11 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
Lie theory harmonic analysis on symmetric spaces  general Plancherel theorems(
)
1 edition published in 2005 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 5 WorldCat member libraries worldwide
Lie theory unitary representations and compactifications of symmetric spaces(
)
1 edition published in 2005 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 5 WorldCat member libraries worldwide
Spherical analysis on harmonic an groups by
JeanPhilippe Anker(
Book
)
3 editions published in 1994 in English and Undetermined and held by 3 WorldCat member libraries worldwide
3 editions published in 1994 in English and Undetermined and held by 3 WorldCat member libraries worldwide
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
Estimations globales du noyau de la chaleur by
Patrick Jacques Ostellari(
Book
)
2 editions published in 2003 in French and held by 2 WorldCat member libraries worldwide
Ce mémoire s'organise autour de deux cadres d'étude : d'une part, celui des espaces symétriques riemanniens non compacts X = G/K, pour lesquels nous prouvons un encadrement optimal et global en les variables d'espace et de temps, du noyau de la chaleur associé à l'opérateur de LaplaceBeltrami L ; d'autre part, dans le cas d'un groupe de Lie semisimple G, nous montrons que tous les souslaplaciens sur G qui induisent l'action de L sur X = G/K présentent des analogies avec L visàvis de l'équation de la chaleur : le bas de leur spectre L^2 est le même, les distances de CarnotCarathéodory associées sont comparables à la métrique riemannienne sur X et, surtout, les noyaux de la chaleur sont tous comparables (en temps grand) au noyau de la chaleur sur X. Nous en déduisons en particulier des encadrements très précis des noyaux de la chaleur dans ce cadre, ainsi que des fonctions de Green correspondantes
2 editions published in 2003 in French and held by 2 WorldCat member libraries worldwide
Ce mémoire s'organise autour de deux cadres d'étude : d'une part, celui des espaces symétriques riemanniens non compacts X = G/K, pour lesquels nous prouvons un encadrement optimal et global en les variables d'espace et de temps, du noyau de la chaleur associé à l'opérateur de LaplaceBeltrami L ; d'autre part, dans le cas d'un groupe de Lie semisimple G, nous montrons que tous les souslaplaciens sur G qui induisent l'action de L sur X = G/K présentent des analogies avec L visàvis de l'équation de la chaleur : le bas de leur spectre L^2 est le même, les distances de CarnotCarathéodory associées sont comparables à la métrique riemannienne sur X et, surtout, les noyaux de la chaleur sont tous comparables (en temps grand) au noyau de la chaleur sur X. Nous en déduisons en particulier des encadrements très précis des noyaux de la chaleur dans ce cadre, ainsi que des fonctions de Green correspondantes
Lie theory. Harmonic analysis on symmetric spaces  general plancherel theorems(
Book
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Lie theory. Unitary representations and compactifications of symmetric spaces(
Book
)
in English and held by 2 WorldCat member libraries worldwide
in 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
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 : Volume 230, Harmonic Analysis on Symmetric Spaces  General Plancherel Theorems by
JeanPhilippe Anker(
)
2 editions 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
2 editions 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
Lie Theory : Volume 229, Unitary Representations and Compactifications of Symmetric Spaces by
JeanPhilippe Anker(
)
2 editions published in 2005 in English and held by 0 WorldCat member libraries worldwide
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  restricting unitary representations to subgroups and decomposing the ensuing representations into irreducibles
2 editions published in 2005 in English and held by 0 WorldCat member libraries worldwide
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  restricting unitary representations to subgroups and decomposing the ensuing representations into irreducibles
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