Dynamical residues of Lorentzian spectral zeta functions

Abstract

We define a dynamical residue which generalizes the Guillemin-Wodzicki residue density of pseudo-differential operators. More precisely, given a Schwartz kernel, the definition refers to Pollicott-Ruelle resonances for the dynamics of scaling towards the diagonal. We apply this formalism to complex powers of the wave operator and we prove that residues of Lorentzian spectral zeta functions are dynamical residues. The residues are shown to have local geometric content as expected from formal analogies with the Riemannian case.

v2: 43 pages, various minor improvements, new appendix on canonical trace density; to appear in J. Éc. polytech. Math

References in corpus (2)

• The noncommutative residue and canonical trace in the light of Stokes' and continuity properties
• Essential self-adjointness of real principal type operators

Cited by in corpus (2)

• A remark on the essential self-adjointness for Klein-Gordon type operators
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