11 Citations
Functional calculus for elliptic operators on noncommutative tori, I
- MathematicsJournal of Pseudo-Differential Operators and Applications
- 2020
In this paper, we introduce a parametric pseudodifferential calculus on noncommutative n -tori which is a natural nest for resolvents of elliptic pseudodifferential operators. Unlike in some previous…
Functional calculus for elliptic operators on noncommutative tori, I
- MathematicsJournal of Pseudo-Differential Operators and Applications
- 2020
In this paper, we introduce a parametric pseudodifferential calculus on noncommutative n-tori which is a natural nest for resolvents of elliptic pseudodifferential operators. Unlike in some previous…
General Rearrangement Lemma for Heat Trace Asymptotic on Noncommutative Tori
- Mathematics
- 2020
We study a technical problem arising from the spectral geometry of noncommutative tori: the small time heat trace asymptotic associated to a general second order elliptic operator. We extend the…
Local invariants of non-commutative tori
- Mathematics
- 2019
We consider a generic curved non-commutative torus extending the notion of conformally deformed non-commutative torus from \cite{Connes-Tretkoff}. In general, a curved non-commutative torus is no…
Pseudodifferential calculus on noncommutative tori, II. Main properties
- MathematicsInternational Journal of Mathematics
- 2019
This paper is the second part of a two-paper series whose aim is to give a detailed description of Connes’ pseudodifferential calculus on noncommutative [Formula: see text]-tori, [Formula: see text].…
Dixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative tori
- MathematicsAdvances in Mathematics
- 2023
Semiclassical Weyl law and exact spectral asymptotics in noncommutative geometry
- Mathematics
- 2021
We prove a Tauberian theorem for singular values of noncommuting operators which allows us to prove exact asymptotic formulas in noncommutative geometry at a high degree of generality. We explain…
Connes’s trace theorem for curved noncommutative tori: Application to scalar curvature
- Mathematics
- 2019
In this paper we prove a version of Connes' trace theorem for noncommutative tori of any dimension~$n\geq 2$. This allows us to recover and improve earlier versions of this result in dimension $n=2$…
Hypergeometric function and Modular Curvature II. Connes-Moscovici functional relation after Lesch's work
- Mathematics
- 2018
In this paper, we initiate a systematic approach for the variational calculus used in the study of modular geometry on noncommutative (two) tori. We introduce several transformations on the space of…
References
SHOWING 1-10 OF 32 REFERENCES
Spectral geometry of functional metrics on noncommutative tori
- Mathematics
- 2018
We introduce a new family of metrics, called functional metrics, on noncommutative tori and study their spectral geometry. We define a class of Laplace type operators for these metrics and study…
The Ricci curvature in noncommutative geometry
- MathematicsJournal of Noncommutative Geometry
- 2019
Motivated by the local formulae for asymptotic expansion of heat kernels in spectral geometry, we propose a definition of Ricci curvature in noncommutative settings. The Ricci operator of an oriented…
Elements of Noncommutative Geometry
- Mathematics
- 2000
This volume covers a wide range of topics including sources of noncommutative geometry; fundamentals of noncommutative topology; K-theory and Morita equivalance; noncommutative integrodifferential…
An Asymmetric Noncommutative Torus
- Mathematics
- 2015
We introduce a family of spectral triples that describe the curved noncommuta- tive two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac…
The Ricci curvature for noncommutative three tori
- MathematicsJournal of Geometry and Physics
- 2020
Scalar Curvature for Noncommutative Four-Tori
- Mathematics
- 2013
In this paper we study the curved geometry of noncommutative 4-tori $\mathbb{T}_\theta^4$. We use a Weyl conformal factor to perturb the standard volume form and obtain the Laplacian that encodes the…
Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals
- MathematicsInternational Journal of Mathematics
- 2019
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…
Modular Curvature for Noncommutative Two-Tori
- Mathematics
- 2011
In this paper we investigate the curvature of conformal deformations by noncommutative Weyl factors of a flat metric on a noncommutative 2-torus, by analyzing in the framework of spectral triples…
Pseudodifferential calculus on noncommutative tori, II. Main properties
- MathematicsInternational Journal of Mathematics
- 2019
This paper is the second part of a two-paper series whose aim is to give a detailed description of Connes’ pseudodifferential calculus on noncommutative [Formula: see text]-tori, [Formula: see text].…
Noncommutative variations on Laplace’s equation
- Mathematics
- 2008
As a first step at developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace's equation and its variants (some of the…