ADIABATIC DECOMPOSITION OF THE -DETERMINANT OF THE DIRAC LAPLACIAN. I. THE CASE OF AN INVERTIBLE TANGENTIAL OPERATOR

DOI10.1081/PDE-120005843zbMath1016.58020arXivmath/0112174OpenAlexW2026832162MaRDI QIDQ3149935

Jinsung Park, Krzysztof P. Wojciechowski

Publication date: 6 February 2003

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

Full work available at URL: https://arxiv.org/abs/math/0112174

zbMATH Keywords

Duhamel's principlespectral boundary conditions\(\zeta\) determinantcompatible operator of Dirac type

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Determinants and determinant bundles, analytic torsion (58J52)

Related Items (10)

Zeta regularized determinants for conic manifolds ⋮ Adiabatic decomposition of the \(\zeta\)-determinant and scattering theory ⋮ Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence ⋮ Functional determinants for the Dirac equation with mixed pseudodifferential boundary conditions over finite cylinders ⋮ Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants ⋮ Zeta functions of Dirac and Laplace-type operators over finite cylinders ⋮ Burghelea-Friedlander-Kappeler’s gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion ⋮ Asymptotic expansions of the zeta-determinants of Dirac Laplacians on a compact manifold with boundary ⋮ Adiabatic decomposition of the \(\xi\)-determinant and Dirichlet to Neumann operator ⋮ On the gluing problem for Dirac operators on manifolds with cylindrical ends

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