Logarithmic terms in asymptotic expansions of heat operator traces

DOI10.1080/03605309808821365zbMath0911.35128OpenAlexW2061445873MaRDI QIDQ4212408

Peter B. Gilkey, Gerd Grubb

Publication date: 24 November 1998

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309808821365

zbMATH Keywords

asymptotic expansioncompact manifold without boundaryelliptic selfadjoint positive pseudo-differential operatorheat operator trace

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Boundary value problems for PDEs with pseudodifferential operators (35S15) Pseudodifferential and Fourier integral operators on manifolds (58J40) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Differential invariants (local theory), geometric objects (53A55)

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Cites Work

• Functional calculus of pseudo-differential boundary problems
• Residues of the eta function for an operator of Dirac type
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Smooth invariants of a Riemannian manifold
• Trace expansions for pseudodifferential boundary problems for Dirac-type operators and more general systems
• Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems
• Zeta and eta functions for Atiyah-Patodi-Singer operators
• Caractérisation de quelques espaces d'interpolation
• Spectral asymmetry and Riemannian Geometry. I
• Analytic Extension of the Trace Associated with Elliptic Boundary Problems