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
MathSciNet review:
3611330
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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
