There are eight-element orthogonal exponentials on the spatial Sierpinski gasket

2018 ◽  
Vol 292 (1) ◽  
pp. 211-226 ◽  
Author(s):  
Qi Wang ◽  
Jian-Lin Li
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Orthogonal Exponentials

THE CARDINALITY OF ORTHOGONAL EXPONENTIAL FUNCTIONS ON THE SPATIAL SIERPINSKI GASKET

Fractals ◽  
2019 ◽  
Vol 27 (04) ◽  
pp. 1950056 ◽  
Author(s):  
JIA ZHENG ◽  
JING-CHENG LIU ◽  
MING-LIANG CHEN
Keyword(s):  
Sierpinski Gasket ◽  
Diagonal Matrix ◽  
The Self ◽  
The Other ◽  
Exponential Functions ◽  
Sierpiński Gasket ◽  
Digit Set ◽  
Orthogonal Exponentials ◽  
Matrix Formula

For the self-affine measures [Formula: see text] generated by a diagonal matrix [Formula: see text] with entries [Formula: see text] and the digit set [Formula: see text], Li showed that there exists an infinite orthogonal exponential functions set in [Formula: see text] if and only if at least two of the three numbers [Formula: see text] are even, and conjectured that there exist at most four mutually orthogonal exponential functions in [Formula: see text] for other cases [J.-L. Li, Non-spectrality of self-affine measures on the spatial Sierpinski gasket, J. Math. Anal. Appl. 432 (2015) 1005–1017]. This conjecture was disproved by Wang and Li through constructing a class of the eight-element orthogonal exponential functions [Q. Wang and J.-L. Li, There are eight-element orthogonal exponentials on the spatial Sierpinski gasket, Math. Nachr. 292 (2019) 211–226]. In this paper, we will show that there are any number of orthogonal exponential functions in [Formula: see text] if two of the three numbers [Formula: see text] are different odd and the other is even.

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 Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

2021 ◽  
Vol 385 ◽  
pp. 107771
Author(s):  
Therese-Marie Landry ◽  
Michel L. Lapidus ◽  
Frédéric Latrémolière
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Spectral Triples

scholarly journals Level sets of harmonic functions on the Sierpiński gasket

2002 ◽  
Vol 40 (2) ◽  
pp. 335-362 ◽  
Author(s):  
Anders Öberg ◽  
Robert S. Strichartz ◽  
Andrew Q. Yingst
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

Design Sierpinski Gasket Antenna for WLAN Application

2007 ◽  
Author(s):  
C.Z.C. Ghani ◽  
M.H.A. Wahab ◽  
N. Abdullah ◽  
S.A Hamzah ◽  
A. Ubin ◽  
...  
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket
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