Raphaël Ponge
YOU?
Author Swipe
View article: Connes' integration and Weyl's laws
Connes' integration and Weyl's laws Open
This paper deals with some questions regarding the notion of integral in the framework of Connes' noncommutative geometry. First, we present a purely spectral theoretic construction of Connes' integral. This answers a question of Alain Con…
View article: Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori
Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori Open
In this paper, we establish Cwikel-type estimates for noncommutative tori for any dimension n ≥ 2. We use them to derive Cwikel–Lieb–Rozenblum inequalities and Lieb–Thirring inequalities for negative eigenvalues of fractional Schrödinger o…
View article: Connes' integration and Weyl's laws
Connes' integration and Weyl's laws Open
This paper deal with some questions regarding the notion of integral in the framework of Connes's noncommutative geometry. First, we present a purely spectral theoretic construction of Connes' integral. This answers a question of Alain Con…
View article: Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger Operators on Curved Noncommutative Tori
Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger Operators on Curved Noncommutative Tori Open
In a previous paper we established Cwikel-type estimates on noncommutative tori and used them to get analogues in this setting of the Cwikel-Lieb-Rozenblum (CLR) and Lieb-Thirring inequalities for negative eigenvalues of fractional Schrödi…
View article: Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger\n Operators on Curved Noncommutative Tori
Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger\n Operators on Curved Noncommutative Tori Open
In a previous paper we established Cwikel-type estimates on noncommutative\ntori and used them to get analogues in this setting of the\nCwikel-Lieb-Rozenblum (CLR) and Lieb-Thirring inequalities for negative\neigenvalues of fractional Schr…
View article: Cwikel Estimates and Negative Eigenvalues of Schroedinger Operators on Noncommutative Tori
Cwikel Estimates and Negative Eigenvalues of Schroedinger Operators on Noncommutative Tori Open
In this paper, we establish Cwikel-type estimates for noncommutative tori for any dimension~$n\geq 2$. We use them to derive Cwikel-Lieb-Rozenblum inequalities and and Lieb-Thirring inequalities for the number of negative eigenvalues of fr…
View article: Periodicity and cyclic homology. Para-$S$-modules and perturbation lemmas
Periodicity and cyclic homology. Para-$S$-modules and perturbation lemmas Open
In this paper, we introduce a paracyclic version of S -modules. These new objects are called para- S -modules . Paracyclic modules and parachain complexes give rise to para- S -modules much in the same way as cyclic modules and mixed compl…
View article: Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results
Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results Open
In this paper we establish uniqueness theorems for the noncommutative residue\nand the canonical trace on pseudodifferential operators on noncommutative tori\nof arbitrary dimension. The former is the unique trace up to constant multiple\n…
View article: Para-S-Modules and Perturbation Lemmas
Para-S-Modules and Perturbation Lemmas Open
In this paper, we introduce a paracyclic version of $S$-modules. These new objects are called \emph{para-$S$-modules}. Paracyclic modules and parachain complexes give rise to para-$S$-modules much in the same way as cyclic modules and mixe…
View article: Noncommutative geometry and conformal geometry. I. Local index formula and conformal invariants
Noncommutative geometry and conformal geometry. I. Local index formula and conformal invariants Open
This paper is part of a series of articles on noncommutative geometry and conformal geometry. In this paper, we reformulate the local index formula in conformal geometry in such a way to take into account the action of conformal diffeomorp…
View article: Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals
Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals Open
This paper is the first part of a two-paper series whose aim is to give a thorough account on Connes' pseudodifferential calculus on noncommutative tori. This pseudodifferential calculus has been used in numerous recent papers, but a detai…
View article: Pseudodifferential calculus on noncommutative tori, II. Main properties
Pseudodifferential calculus on noncommutative tori, II. Main properties Open
This paper is the 2nd part of a two-paper series whose aim is to give a detailed description of Connes' pseudodifferential calculus on noncommutative $n$-tori, $n\geq 2$. We make use of the tools introduced in the 1st part to deal with the…
View article: Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates
Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates Open
This paper is a sequel of arxiv:1709.09045 and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold equipped with a filtration by subbundles of the tangent bundle wh…
View article: Privileged coordinates and tangent groupoid for Carnot manifolds
Privileged coordinates and tangent groupoid for Carnot manifolds Open
This paper is part of a series of papers on the construction of a full hypoelliptic pseudodifferential calculus on Carnot manifolds. The first goal of the paper is to produce a refinement of privileged coordinates for Carnot manifolds for …