## 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…