AbstractLetGbe a connected compact type Lie group equipped with anAdG-invariant inner product on the Lie algebra g ofG. Given this data there is a well known left invariant “H1-Riemannian structure” on L=L(G)—the infinite dimensional group of continuous based loops inG. Using this Riemannian structure, we define and construct a “heat kernel”νT(g0, ·) associated to the Laplace–Beltrami operator on L(G). HereT>0,g0∈L(G), andνT(g0,·) is a certain probability measure on L(G). For fixedg0∈L(G) andT>0, we use the measureνT(g0,·) and the Riemannian structure on L(G) to construct a “classical” pre-Dirichlet form. The main theorem of this paper asserts that this pre-Dirichlet form admits a logarithmic Sobolev inequality
AbstractWe continue our study of the logarithmic Sobolev inequality of Gross and its connections wit...
AbstractWe prove log-Sobolev inequalities for Hörmander type generators in infinite dimensions and p...
Gong F, Röckner M, Liming W. Poincaré inequality for weighted first order Sobolev spaces on loop spa...
AbstractLetGbe a connected compact type Lie group equipped with anAdG-invariant inner product on the...
AbstractLet G be a compact Lie group. Denote by m the Brownian bridge measure on the loop group Y ≡ ...
AbstractIn this paper we will prove the logarithmic Sobolev inequality on free loop groups for vario...
AbstractWe obtain a log-Sobolev inequality with a neat and explicit potential for the gradient on a ...
Dans cette note, nous obtenons une inégalité de Sobolev logarithmique nouvelle pour le noyau de la c...
AbstractLet E be the loop space over a compact connected Riemannian manifold with a torsion skew sym...
We show that the Laplacian on the loop space over a class of Riemannian manifolds has a spectral gap...
International audienceWe present a finite dimensional version of the logarithmic Sobolev inequality ...
We obtain a martingale representation theorem for differentiable functions on loop space over a comp...
AbstractLet X denote a simply connected compact Riemannian symmetric space, U the universal covering...
AbstractLet G be a compact Lie group, L(G) the associated loop group, ω the canonical symplectic for...
AbstractLogarithmic Sobolev inequalities with potential functions on loop spaces were proved by L. G...
AbstractWe continue our study of the logarithmic Sobolev inequality of Gross and its connections wit...
AbstractWe prove log-Sobolev inequalities for Hörmander type generators in infinite dimensions and p...
Gong F, Röckner M, Liming W. Poincaré inequality for weighted first order Sobolev spaces on loop spa...
AbstractLetGbe a connected compact type Lie group equipped with anAdG-invariant inner product on the...
AbstractLet G be a compact Lie group. Denote by m the Brownian bridge measure on the loop group Y ≡ ...
AbstractIn this paper we will prove the logarithmic Sobolev inequality on free loop groups for vario...
AbstractWe obtain a log-Sobolev inequality with a neat and explicit potential for the gradient on a ...
Dans cette note, nous obtenons une inégalité de Sobolev logarithmique nouvelle pour le noyau de la c...
AbstractLet E be the loop space over a compact connected Riemannian manifold with a torsion skew sym...
We show that the Laplacian on the loop space over a class of Riemannian manifolds has a spectral gap...
International audienceWe present a finite dimensional version of the logarithmic Sobolev inequality ...
We obtain a martingale representation theorem for differentiable functions on loop space over a comp...
AbstractLet X denote a simply connected compact Riemannian symmetric space, U the universal covering...
AbstractLet G be a compact Lie group, L(G) the associated loop group, ω the canonical symplectic for...
AbstractLogarithmic Sobolev inequalities with potential functions on loop spaces were proved by L. G...
AbstractWe continue our study of the logarithmic Sobolev inequality of Gross and its connections wit...
AbstractWe prove log-Sobolev inequalities for Hörmander type generators in infinite dimensions and p...
Gong F, Röckner M, Liming W. Poincaré inequality for weighted first order Sobolev spaces on loop spa...