Determinants of classical SG‐pseudodifferential operators
Copyright policy )Determinants of classical SG‐pseudodifferential operators
We introduce a generalized trace functional TR in the spirit of Kontsevich and Vishik's canonical trace for classical SG‐pseudodifferential operators on and suitable manifolds, using a finite‐part integral regularization technique. This allows us to define a zeta‐regularized determinant for parameter‐elliptic operators , , . For , the asymptotics of as and of as are derived. For suitable pairs we show that coincides with the so‐called relative determinant .
- University of Hannover Germany
- University of Turin Italy
Kontsevich-Vishik trace, regularized determinant, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Pseudodifferential operators; Kontsevich-Vishik trace; Regularized determinant, Primary: 47G30, Secondary: 47A10, 47L15, 58J42, Pseudodifferential and Fourier integral operators on manifolds, FOS: Mathematics, Operator algebras with symbol structure, Pseudodifferential operators, Spectrum, resolvent, pseudodifferential operators, Noncommutative global analysis, noncommutative residues, Analysis of PDEs (math.AP)
Kontsevich-Vishik trace, regularized determinant, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Pseudodifferential operators; Kontsevich-Vishik trace; Regularized determinant, Primary: 47G30, Secondary: 47A10, 47L15, 58J42, Pseudodifferential and Fourier integral operators on manifolds, FOS: Mathematics, Operator algebras with symbol structure, Pseudodifferential operators, Spectrum, resolvent, pseudodifferential operators, Noncommutative global analysis, noncommutative residues, Analysis of PDEs (math.AP)
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