46 citations · 191 across the 47 of their papers we have counts for
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Sobolev Orthogonal Polynomials on the Sierpinski Gasket
Qingxuan Jiang, Tian Lan, Kasso Okoudjou +4
We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket (). These orthogonal polynomials arise through the Gram-Schmidt orthogonalisation process applied…
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…
Polynomials on the Sierpinski Gasket with Respect to Different Laplacians which are Symmetric and Self-Similar
Christian Loring, W. Jacob Ogden, Ely Sandine +1
We study the analogue of polynomials (solutions to for some ) on the Sierpinski gasket () with respect to a family of symmetric, self-similar Laplacians const…
Sparse Averages of Partial Sums of Fourier Series
Ethan Goolish, Robert S. Strichartz
We study convergence properties of sparse averages of partial sums of Fourier series of continuous functions. By sparse averages, we are considering an increasing sequences of inte…
Defining Curvature as a Measure via Gauss-Bonnet on Certain Singular Surfaces
Robert S Strichartz
We show how to define curvature as a measure using the Gauss-Bonnet Theorem on a family of singular surfaces obtained by gluing together smooth surfaces along boundary curves. We f…