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

2016 ◽  
Vol 145 (5) ◽  
pp. 2183-2198 ◽  
Author(s):  
Marius Ionescu ◽  
Kasso A. Okoudjou ◽  
Luke G. Rogers
Keyword(s):  
Spectral Properties ◽  
Differential Operators ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Pseudo Differential Operators

scholarly journals COMB GRAPHS AND SPECTRAL DECIMATION

2009 ◽  
Vol 51 (1) ◽  
pp. 71-81 ◽  
Author(s):  
JONATHAN JORDAN
Keyword(s):  
Adjacency Matrix ◽  
Spectral Properties ◽  
Sierpinski Gasket ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Spectral Similarity ◽  
Similarity Relationship ◽  
Adjacency Matrices ◽  
Similarity Operators ◽  
Math Phys

AbstractWe investigate the spectral properties of matrices associated with comb graphs. We show that the adjacency matrices and adjacency matrix Laplacians of the sequences of graphs show a spectral similarity relationship in the sense of work by L. Malozemov and A. Teplyaev (Self-similarity, operators and dynamics,Math. Phys. Anal. Geometry6(2003), 201–218), and hence these sequences of graphs show a spectral decimation property similar to that of the Laplacians of the Sierpiński gasket graph and other fractal graphs.

scholarly journals Dimer Coverings on the Sierpinski Gasket

2008 ◽  
Vol 131 (4) ◽  
pp. 631-650 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 65
Author(s):  
Benjamin Akers ◽  
Tony Liu ◽  
Jonah Reeger
Keyword(s):  
Radial Basis Function ◽  
Hilbert Transform ◽  
Basis Function ◽  
Differential Operators ◽  
Convergence Rates ◽  
Traveling Wave Solutions ◽  
Algebraic Decay ◽  
Pseudo Differential Operators ◽  
Radial Basis ◽  
The Hilbert Transform

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.

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