Complex powers of abstract pseudodifferential operators

Authors

  • M. A. Fahrenwaldt Maxwell Institute for Mathematical Sciences, School of Mathematical & Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom

DOI:

Keywords:

Complex powers, abstract pseudodifferential operators, noncommutative residue, zeta function, heat trace, index theory

Abstract

Under suitable assumptions, we show that the abstract pseudodifferen\-tial operators introduced by Connes and Moscovici possess complex powers that belong to this class of operators. We analyse several spectral functions obtained via the (super)trace including the zeta function and the heat trace. We present examples showing that the analysis is explicit and tractable.

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Published

2018-12-25

Issue

Vol. 24 No. 4 (2018)

Section

Articles

How to Cite

Fahrenwaldt, M. A. “Complex Powers of Abstract Pseudodifferential Operators”. Methods of Functional Analysis and Topology, vol. 24, no. 4, Dec. 2018, pp. 305-38, https://zen.imath.kiev.ua/index.php/mfat/article/view/703.