Abstract
In this note we study the analytical index of pseudo-differential operators by using the notion of (infinite dimensional) operator-valued symbols (in the sense of Ruzhansky and Turunen). Our main tools will be the McKean–Singer index formula together with the operator-valued functional calculus developed here.
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Acknowledgements
I would like to thank Alexander Cardona and Michael Ruzhansky for various discussions. I also would like to thanks Julio Delgado who has suggested me a gap in the proof of Proposition 4.8 in a previous version of this document. The author is indebted with the referee of this paper by his/her asserted suggestions which helped to improve the manuscript.
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Cardona, D. On the index of pseudo-differential operators on compact Lie groups. J. Pseudo-Differ. Oper. Appl. 10, 285–305 (2019). https://doi.org/10.1007/s11868-018-0261-0
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DOI: https://doi.org/10.1007/s11868-018-0261-0