Dynamical residues of Lorentzian spectral zeta functions
Analysis of PDEs
2024-12-05 v2 Mathematical Physics
Dynamical Systems
math.MP
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.
Keywords
Cite
@article{arxiv.2108.07529,
title = {Dynamical residues of Lorentzian spectral zeta functions},
author = {Nguyen Viet Dang and Michał Wrochna},
journal= {arXiv preprint arXiv:2108.07529},
year = {2024}
}
Comments
v2: 43 pages, various minor improvements, new appendix on canonical trace density; to appear in J. \'Ec. polytech. Math