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Complex powers of abstract pseudodifferential operators


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.

Key words: Complex powers, abstract pseudodifferential operators, noncommutative residue, zeta function, heat trace, index theory.

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TitleComplex powers of abstract pseudodifferential operators
SourceMethods Funct. Anal. Topology, Vol. 24 (2018), no. 4, 305-338
MilestonesReceived 14/12/2017; Revised 31/05/2018
CopyrightThe Author(s) 2018 (CC BY-SA)

Authors Information

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

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M. A. Fahrenwaldt, Complex powers of abstract pseudodifferential operators, Methods Funct. Anal. Topology 24 (2018), no. 4, 305-338.


@article {MFAT1113,
    AUTHOR = {M. A. Fahrenwaldt},
     TITLE = {Complex powers of abstract pseudodifferential operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {24},
      YEAR = {2018},
    NUMBER = {4},
     PAGES = {305-338},
      ISSN = {1029-3531},
       URL = {},


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