MAGNETIC LAPLACIANS OF LOCALLY EXACT FORMS ON THE SIERPINSKI GASKET

被引：3

作者：

Hyde, Jessica ^{[1
]}

Kelleher, Daniel ^{[2
]}

Moeller, Jesse ^{[3
]}

Rogers, Luke ^{[4
]}

Seda, Luis ^{[5
]}

机构：

[1] MIT, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] Univ Alberta, Edmonton, AB, Canada

[3] Univ Nebraska, Lincoln, NE USA

[4] Univ Connecticut, Storrs, CT 06269 USA

[5] Univ Puerto Rico Mayaguez, Mayaguez, PR USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2017年 / 16卷 / 06期

基金：

美国国家科学基金会;

关键词：

Analysis on fractals; Sierpinski gasket; magnetic form; Schrodinger operator; SELF-SIMILAR FRACTALS; DIRICHLET FORMS; SCHRODINGER-EQUATION; SPECTRUM; SPACES; DERIVATIONS; FRACTAFOLDS; OPERATORS; GRAPHS; FIELD;

D O I：

10.3934/cpaa.2017113

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give an explicit construction of a magnetic Schrodinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at infinity, and it is shown that the asymptotic distribution of eigenvalues is the same as that for the Laplacian. Most eigenfunctions may be computed using gauge transformations corresponding to the magnetic field and the remainder of the spectrum may be approximated to arbitrary precision by using a sequence of approximations by magnetic operators on finite graphs.

引用

页码：2299 / 2319

页数：21

共 42 条

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