4 citations · 20 across the 27 of their papers we have counts for
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Spectral analysis beyond on Sierpinski lattices
Shiping Cao, Yiqi Huang, Hua Qiu +2
We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of , remains the same for any …
A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket
Shiping Cao, Shuangping Li, Robert S. Strichartz +1
We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special…
The Mathieu Differential Equation and Generalizations to Infinite Fractafolds
Shiping Cao, Anthony Coniglio, Xueyan Niu +2
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by c…
Sobolev spaces on p.c.f. self-similar sets: critical orders and atomic decompositions
Shiping Cao, Hua Qiu
We consider the Sobolev type spaces with , where is a post-critically finite self-similar set with the natural boundary. Firstly, we compare different classes…
Sobolev spaces and trace theorem on the Sierpinski gasket
Shiping Cao, Hua Qiu
On the Sierpinski gasket , we consider Sobolev spaces associated with the standard Laplacian with order . When ,…