45 citations · 146 across the 29 of their papers we have counts for
4 papers · 1 filter
On a theorem of Grigor'yan, Hu and Lau
Luke G. Rogers
We refine a result of Grigor'yan, Hu and Lau to give a moment condition on a heat kernel which characterizes the critical exponent at which a family of Besov spaces associated to t…
Sobolev Algebra Counterexamples
Thierry Coulhon, Luke G. Rogers
In the Euclidean setting the Sobolev spaces are algebras for the pointwise product when and . This property has recently been extended…
Power dissipation in fractal AC circuits
Joe P. Chen, Luke G. Rogers, Loren Anderson +8
We extend Feynman's analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have c…
Magnetic Laplacians of locally exact forms on the Sierpinski Gasket
Jessica Hyde, Daniel J. Kelleher, Jesse Moeller +2
We give a mathematically rigorous construction of a magnetic Schrödinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The opera…