Journal of Operator Theory

Volume 80, Issue 1, Summer 2018 pp. 113-124.

Taylor asymptotics of spectral action functionals

Authors: Anna Skripka
Author institution: Department of Mathematics and Statistics, University of New Mexico, 400 Yale Blvd NE, MSC01 1115, Albuquerque, NM 87131, U.S.A.

Summary: We establish a Taylor asymptotic expansion of the spectral action functional on self-adjoint operators $V\mapsto\tau(f(H+V))$ with remainder $\mathcal{O} (\|f^{(n)}\|_\infty\|V\|^n )$ and derive an explicit representation for the remainder in terms of spectral shift functions. For this expansion we assume only that $H$ has $\tau$-compact resolvent and $V$ is a bounded perturbation; in particular, neither summability of $V$ nor of the resolvent of $H$ is required.

DOI: http://dx.doi.org/10.7900/jot.2017jun19.2158
Keywords: spectral action, perturbation theory

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