Noncommutative residues for pseudo-differential operators on the noncommutative two-torus

DOI10.1007/s11868-011-0030-9zbMath1266.58010OpenAlexW2013164360MaRDI QIDQ1758378

Farzad Fathizadeh, Man-Wah Wong

Publication date: 9 November 2012

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11868-011-0030-9

zbMATH Keywords

noncommutative toruspseudo-differential operatorsnoncommutative residues

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Noncommutative global analysis, noncommutative residues (58J42)

Related Items (17)

Spectral action for Bianchi type-IX cosmological models ⋮ Curvature of the determinant line bundle for the noncommutative two torus ⋮ A two dimensional Adler-Manin trace and bi-singular operators ⋮ Spectral metric and Einstein functionals ⋮ Weyl's law and Connes' trace theorem for noncommutative two tori ⋮ Curvature in noncommutative geometry ⋮ Advances in Dixmier traces and applications ⋮ Connes’s trace theorem for curved noncommutative tori: Application to scalar curvature ⋮ Curved noncommutative torus and Gauss–Bonnet ⋮ Gravity, non-commutative geometry, and the Wodzicki residue ⋮ The canonical trace and the noncommutative residue on the noncommutative torus ⋮ Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals ⋮ Pseudodifferential calculus on noncommutative tori, II. Main properties ⋮ Noncommutative residue and canonical trace on noncommutative tori. Uniqueness results ⋮ On the scalar curvature for the noncommutative four torus ⋮ On the Chern-Gauss-Bonnet theorem and conformally twisted spectral triples for \(C^*\)-dynamical systems ⋮ Scalar curvature for noncommutative four-tori

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• Algebraic aspects of nonlinear differential equations
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• A new proof of Weyl's formula on the asymptotic distribution of eigenvalues
• Elliptic mixed, transmission and singular crack problems
• The noncommutative residue for manifolds with boundary
• The Gauss-Bonnet Theorem for the noncommutative two torus
• Mellin Operators with Asymptotics on Manifolds with Corners

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