Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians

Sze-Man Ngai

Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

<p> We observe that some self-similar measures de&filig;ned by &filig;nite or in&filig;nite iterated function systems with overlaps satisfy certain “bounded measure type condition”, which allows us to extract useful measure-theoretic properties of iterates of the measure. We develop a technique to obtain, under this condition, a closed formula for the spectral dimension of the Laplacian. This is a joint work with Wei Tang and Yuanyuan Xie.</p>

Original language	American English
State	Published - Feb 3 2017
Event	Harmonic Analysis and Geometry of Fractal Sets (HAFS) - Duration: Feb 3 2017 → …

Conference

Conference	Harmonic Analysis and Geometry of Fractal Sets (HAFS)
Period	02/3/17 → …

Keywords

Fractal Laplacians
One-dimensional
Spectral asymptotics

DC Disciplines

Mathematics
Physical Sciences and Mathematics

Access to Document

https://u.osu.edu/hafs2017/files/2016/11/Schedule_Feb2017_fancy-t835ud.pdf

Cite this

@conference{45ef3dfff49c41a9b3e34c41b62ed174,

title = "Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians",

abstract = " We observe that some self-similar measures de&filig;ned by &filig;nite or in&filig;nite iterated function systems with overlaps satisfy certain “bounded measure type condition”, which allows us to extract useful measure-theoretic properties of iterates of the measure. We develop a technique to obtain, under this condition, a closed formula for the spectral dimension of the Laplacian. This is a joint work with Wei Tang and Yuanyuan Xie.",

keywords = "Fractal Laplacians, One-dimensional, Spectral asymptotics",

author = "Sze-Man Ngai",

year = "2017",

month = feb,

day = "3",

language = "American English",

note = "Harmonic Analysis and Geometry of Fractal Sets (HAFS) ; Conference date: 03-02-2017",

}

TY - CONF

T1 - Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians

AU - Ngai, Sze-Man

PY - 2017/2/3

Y1 - 2017/2/3

N2 - We observe that some self-similar measures de&filig;ned by &filig;nite or in&filig;nite iterated function systems with overlaps satisfy certain “bounded measure type condition”, which allows us to extract useful measure-theoretic properties of iterates of the measure. We develop a technique to obtain, under this condition, a closed formula for the spectral dimension of the Laplacian. This is a joint work with Wei Tang and Yuanyuan Xie.

AB - We observe that some self-similar measures de&filig;ned by &filig;nite or in&filig;nite iterated function systems with overlaps satisfy certain “bounded measure type condition”, which allows us to extract useful measure-theoretic properties of iterates of the measure. We develop a technique to obtain, under this condition, a closed formula for the spectral dimension of the Laplacian. This is a joint work with Wei Tang and Yuanyuan Xie.

KW - Fractal Laplacians

KW - One-dimensional

KW - Spectral asymptotics

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpres/369

UR - https://u.osu.edu/hafs2017/files/2016/11/Schedule_Feb2017_fancy-t835ud.pdf

M3 - Presentation

T2 - Harmonic Analysis and Geometry of Fractal Sets (HAFS)

Y2 - 3 February 2017

ER -

Spectral Asymptotics of a Class of One-Dimensional Fractal Laplacians

Abstract

Conference

Keywords

DC Disciplines

Access to Document

Other files and links

Fingerprint

Cite this