45 citations · 45 across the 4 of their papers we have counts for
7 papers
The Strong Maximum Principle for Schrödinger operators on fractals
Marius V. Ionescu, Kasso A. Okoudjou, Luke G. Rogers
We prove a strong maximum principle for Schrödinger operators defined on a class of fractal sets and their blowups without boundary. Our primary interest is in weaker regularity co…
The "Hot Spots" Conjecture on the Vicsek Set
Marius Ionescu, Thomas L. Savage
We prove the Hot Spot conjecture on the Vicsek set. Specifically, we show that every eigenfunction of the second smallest eigenvalue of the Neumann Laplacian on the Vicsek set atta…
Some spectral properties of pseudo-differential operators on the Sierpinski Gasket
Marius Ionescu, Kasso A. Okoudjou, Luke G. Rogers
We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Our results used in a fundamental way the…
Pseudo-differential Operators on Fractals
Marius Ionescu, Luke G. Rogers, Robert S. Strichartz
We define and study pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian es…
Derivations and Dirichlet forms on fractals
Marius Ionescu, Luke G. Rogers, Alexander Teplyaev
We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a n…
Complex Powers of the Laplacian on Affine Nested Fractals as Calderón-Zygmund operators
Marius Ionescu, Luke Rogers
We give the first natural examples of Calderón-Zygmund operators in the theory of analysis on post-critically finite self-similar fractals. This is achieved by showing that the pur…