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


Authors: Marius Ionescu, Kasso A. Okoudjou and Luke G. Rogers
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
Published electronically: December 15, 2016
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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.


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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
Email: kasso@math.umd.edu

Luke G. Rogers
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009
Email: rogers@math.uconn.edu

DOI: https://doi.org/10.1090/proc/13512
Keywords: Analysis on fractals, localized eigenfunctions, Sierpi\'nski gasket, Sz\"ego limit theorem
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