34 citations · 206 across the 41 of their papers we have counts for
43 papers
Functional Calculus on Noncommutative Tori, II. Complex Powers, Logarithms, and Sectorial Projections
Gihyun Lee, Raphael Ponge
This paper develops a systematic theory of complex powers, logarithms, and sectorial projections of elliptic pseudodifferential operators on noncommutative tori, extending to this…
Noncommutative Geometry, Spectral Asymptotics, and Semiclassical Analysis
Raphael Ponge
Semiclassical analysis and noncommutative geometry are two pillars of quantum theory. It is only recently that bridges between them have been emerging. In this monograph, we combin…
Weyl's laws and Connes' integration formulas for matrix-valued -Orlicz potentials
Raphael Ponge
Thanks to the Birman-Schwinger principle, Weyl's laws for Birman-Schwinger operators yields semiclassical Weyl's laws for the corresponding Schrödinger operators. In a recent prepr…
Connes' integration and Weyl's laws
Raphael Ponge
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 constructio…
Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger Operators on Curved Noncommutative Tori
Edward McDonald, Raphael Ponge
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…
Cwikel Estimates and Negative Eigenvalues of Schroedinger Operators on Noncommutative Tori
Edward McDonald, Raphael Ponge
In this paper, we establish Cwikel-type estimates for noncommutative tori for any dimension~. We use them to derive Cwikel-Lieb-Rozenblum inequalities and and Lieb-Thirrin…