TEMPERED OPERATORS AND THE HEAT KERNEL AND COMPLEX POWERS OF ELLIPTIC PSEUDODIFFERENTIAL OPERATORS

DOI10.1081/PDE-100106134zbMath1008.58019MaRDI QIDQ2769488

Paul Loya

Publication date: 25 March 2003

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

zbMATH Keywords

Laplace transformMellin transformmanifold with cornersasymptotic expansionheat operatorindex theorem\(b\)-pseudodifferential operators\(b\)-eta function\(b\)-zeta functioncomplex powers of operatorsholomorphically tempered operators

Mathematics Subject Classification ID

Heat equation (35K05) Index theory and related fixed-point theorems on manifolds (58J20) Pseudodifferential and Fourier integral operators on manifolds (58J40) Eta-invariants, Chern-Simons invariants (58J28) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items

Complex Powers and Non-compact Manifolds, The index of \(b\)-pseudodifferential operators on manifolds with corners, Resolvents and complex powers of semiclassical cone operators, Complex powers of differential operators on manifolds with conical singularities, Asymptotic properties of the heat kernel on conic manifolds, Weyl laws on open manifolds, On the Logarithm Component in Trace Defect Formulas, Mapping properties of the heat operator on edge manifolds, Cusp geometry and the cobordism invariance of the index, The structure of the resolvent of elliptic pseudodifferential operators, Boundary problems for Dirac-type operators on manifolds with multi-cylindrical end boundaries, On Carvalho’s $K$-theoretic formulation of the cobordism invariance of the index, On the gluing problem for Dirac operators on manifolds with cylindrical ends

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