Analyse harmonique hyperbolique : représentations et contractions des groupes
Analyse harmonique non linéaire
Analyse harmonique sur les groupes algébriques complexes : formule de Plancherel
Analyse spectrale des formes automorphes et séries d'Eisenstein.
Analysis in matrix space and Speh's representations.
Analysis of joint spectral multipliers on Lie groups of polynomial growth
We study the problem of -boundedness () of operators of the form for a commuting system of self-adjoint left-invariant differential operators on a Lie group of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when is a homogeneous group and are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.
Analysis of second order differential operators on Heisenberg groups. I.
Analysis of second order differential operators with complex coefficients on the Heisenberg group.
Analysis of two step nilsequences
Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’s Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for two step nilsequences and give a classification scheme for them.
Analysis on compact Lie groups of large dimension and on connected compact groups
The study of Gaussian convolution semigroups is a subject at the crossroad between abstract and concrete problems in harmonic analysis. This article suggests selected open problems that are in large part motivated by joint work with Alexander Bendikov.
Analysis on the Heisenberg Group and Estimates for Functions in Hardy Classes of Several Complex Variables.
Analytic continuation for Flensted-Jensen Representations.
Analytic functions and linearly ordered groups
Analytic measure and quasi-invariant measure
Analytic potential theory over the -adics
Over a non-archimedean local field the absolute value, raised to any positive power , is a negative definite function and generates (the analogue of) the symmetric stable process. For , this process is transient with potential operator given by M. Riesz’ kernel. We develop this potential theory purely analytically and in an explicit manner, obtaining special features afforded by the non-archimedean setting ; e.g. Harnack’s inequality becomes an equality.
Analytic sets in the theory of commutative semigroups
A problem about representations of countable, commutative semigroups leads to an analytic non-Borel set.
Analytic structures on representation spaces of reductive groups.
Analyticity for certain solutions of non-hypoelliptic differential operators on the Heisenberg group
Analytische Vektoren von Faltungshalbgruppen. I.
Analytische Vektoren von Faltungshalbgruppen II. Funktionenräume auf lokalkompakten Gruppen.