## Some spectral properties of pseudo-differential operators on the Sierpiński gasket

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- by Marius Ionescu, Kasso A. Okoudjou and Luke G. Rogers PDF
- Proc. Amer. Math. Soc.
**145**(2017), 2183-2198 Request permission

## Abstract:

We prove versions of the strong Szegö limit theorem for certain classes of pseudo-differential operators defined on the Sierpiński gasket. Our results use in a fundamental way the existence of localized eigenfunctions for the Laplacian on this fractal.## References

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## Additional Information

**Marius Ionescu**- Affiliation: Department of Mathematics, United States Naval Academy, Annapolis, Maryland 21402-5002
- Email: ionescu@usna.edu
**Kasso A. Okoudjou**- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
- MR Author ID: 721460
- ORCID: setImmediate$0.18192135121667974$6
- Email: kasso@math.umd.edu
**Luke G. Rogers**- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009
- MR Author ID: 785199
- Email: rogers@math.uconn.edu
- Received by editor(s): June 19, 2014
- Received by editor(s) in revised form: July 23, 2016
- Published electronically: December 15, 2016
- Additional Notes: The first author was supported by a grant from the Simons Foundation (#209277). He would like to thank Kasso Okoudjou and the Department of Mathematics at the University of Maryland, College Park, and the Norbert-Wiener Center for Harmonic Analysis and Applications for their hospitality.

The second author was supported by a grant from the Simons Foundation (#319197) and ARO grant W911NF1610008. - Communicated by: Alexander Iosevich
- Journal: Proc. Amer. Math. Soc.
**145**(2017), 2183-2198 - MSC (2010): Primary 35P20, 28A80; Secondary 42C99, 81Q10
- DOI: https://doi.org/10.1090/proc/13512
- MathSciNet review: 3611330