Classification of traces and hypertraces on spaces of classical pseudodifferential operators

DOI10.4171/JNCG/123zbMath1272.58015arXiv1011.3238MaRDI QIDQ355363

Matthias Lesch, Carolina Neira Jiménez

Publication date: 24 July 2013

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.3238

zbMATH Keywords

canonical tracenoncommutative residueclassical pseudodifferential operatorhomogeneous differential formregularized integralsymplectic conesymplectic residuetrace functional

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Pseudodifferential and Fourier integral operators on manifolds (58J40) Noncommutative global analysis, noncommutative residues (58J42)

Related Items (10)

The geometry of loop spaces. II: Characteristic classes. ⋮ Weyl's law and Connes' trace theorem for noncommutative two tori ⋮ Wodzicki residue for operators on manifolds with cylindrical ends ⋮ Equivariant, string and leading order characteristic classes associated to fibrations ⋮ Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras ⋮ Determinants of classical SG‐pseudodifferential operators ⋮ The canonical trace and the noncommutative residue on the noncommutative torus ⋮ Noncommutative residue and canonical trace on noncommutative tori. Uniqueness results ⋮ On the scalar curvature for the noncommutative four torus ⋮ Chern–Weil Theory for Certain Infinite-Dimensional Lie Groups

Cites Work

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• The homology of algebras of pseudo-differential symbols and the noncommutative residue
• Residue traces for certain algebras of Fourier integral operators
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems
• A new proof of Weyl's formula on the asymptotic distribution of eigenvalues
• Fourier integral operators. I
• The noncommutative residue for manifolds with boundary
• Lectures on symplectic geometry

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