Spectral Asymptotics of One-Dimensional Fractal Laplacians in the Absence of Second-Order Identities

Sze-Man Ngai

Spectral Asymptotics of One-Dimensional Fractal Laplacians in the Absence of Second-Order Identities

Sze-Man Ngai

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

We observe that some self-similar measures deﬁned by ﬁnite or inﬁnite 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 a closed formula for the spectral dimension of the Laplacian deﬁned by self-similar measures satisfying this condition.

Original language	American English
State	Published - Dec 26 2016
Event	Tsinghua Sanya Mathematics Forum: Analysis on Fractals and Graphs Workshop - Duration: Dec 26 2016 → …

Conference

Conference	Tsinghua Sanya Mathematics Forum: Analysis on Fractals and Graphs Workshop
Period	12/26/16 → …

Disciplines

Mathematics
Physical Sciences and Mathematics

Keywords

Asymptotics
Laplacians
One-dimensional fractal laplacians
Second-ord identities

Cite this

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title = "Spectral Asymptotics of One-Dimensional Fractal Laplacians in the Absence of Second-Order Identities",

abstract = "We observe that some self-similar measures deﬁned by ﬁnite or inﬁnite 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 a closed formula for the spectral dimension of the Laplacian deﬁned by self-similar measures satisfying this condition.",

keywords = "Asymptotics, Laplacians, One-dimensional fractal laplacians, Second-ord identities",

author = "Sze-Man Ngai",

year = "2016",

month = dec,

day = "26",

language = "American English",

note = "Tsinghua Sanya Mathematics Forum: Analysis on Fractals and Graphs Workshop ; Conference date: 26-12-2016",

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TY - CONF

T1 - Spectral Asymptotics of One-Dimensional Fractal Laplacians in the Absence of Second-Order Identities

AU - Ngai, Sze-Man

PY - 2016/12/26

Y1 - 2016/12/26

N2 - We observe that some self-similar measures deﬁned by ﬁnite or inﬁnite 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 a closed formula for the spectral dimension of the Laplacian deﬁned by self-similar measures satisfying this condition.

AB - We observe that some self-similar measures deﬁned by ﬁnite or inﬁnite 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 a closed formula for the spectral dimension of the Laplacian deﬁned by self-similar measures satisfying this condition.

KW - Asymptotics

KW - Laplacians

KW - One-dimensional fractal laplacians

KW - Second-ord identities

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpres/19

M3 - Presentation

T2 - Tsinghua Sanya Mathematics Forum: Analysis on Fractals and Graphs Workshop

Y2 - 26 December 2016

ER -

Spectral Asymptotics of One-Dimensional Fractal Laplacians in the Absence of Second-Order Identities

Abstract

Conference

Disciplines

Keywords

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