Zobrazeno 1 - 10
of 138
pro vyhledávání: '"Kelleher, Daniel"'
We prove existence of a measurable Riemannian structure on higher-dimensional harmonic Sierpinski gasket fractals and deduce Gaussian heat kernel bounds in the geodesic metric. Our proof differs from that given by Kigami for the usual Sierpinski gask
Externí odkaz:
http://arxiv.org/abs/1703.03380
Autor:
Kelleher, Daniel J.
This paper introduces a notion of differential forms on closed, potentially fractal, subsets of Euclidean space by defining pointwise cotangent spaces using the restriction of $C^1$ functions to this set. Aspects of cohomology are developed: it is sh
Externí odkaz:
http://arxiv.org/abs/1701.02684
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Autor:
Baudoin, Fabrice, Kelleher, Daniel J.
We develop a general framework on Dirichlet spaces to prove a weak form of the Bakry-\'Emery estimate and study its consequences. This estimate may be satisfied in situations, like metric graphs, where generalized notions of Ricci curvature lower bou
Externí odkaz:
http://arxiv.org/abs/1604.02520
We give a mathematically rigorous construction of a magnetic Schr\"odinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at $\infty$, and
Externí odkaz:
http://arxiv.org/abs/1604.01340
We prove Barlow--Bass type resistance estimates for two random walks associated with repeated barycentric subdivisions of a triangle. If the random walk jumps between the centers of triangles in the subdivision that have common sides, the resistance
Externí odkaz:
http://arxiv.org/abs/1505.03161
Publikováno v:
J. Phys. A 49 (2016), no. 16, 165206, 36 pp
This article studies potential theory and spectral analysis on compact metric spaces, which we refer to as fractal quantum graphs. These spaces can be represented as a (possibly infinite) union of 1-dimensional intervals and a totally disconnected (p
Externí odkaz:
http://arxiv.org/abs/1408.4658
Autor:
Kelleher, Daniel, Gupta, Nikhar, Margenot, Maxwell, Marsh, Jason, Oakley, William, Teplyaev, Alexander
Publikováno v:
Commun. Pure Appl. Anal. 14 (2015), no. 6, 2509-2533
This article develops analysis on fractal $3N$-gaskets, a class of post-critically finite fractals which include the Sierpinski triangle for $N=1$, specifically properties of the Laplacian $\Delta$ on these gaskets. We first prove the existence of a
Externí odkaz:
http://arxiv.org/abs/1408.4294
Publikováno v:
Noncommut. Geom. 9 (2015), 359-390
The article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance form is given and the space is compact in resistance metric, then the
Externí odkaz:
http://arxiv.org/abs/1309.5937
Using the standard tools of Daniell-Stone integrals, Stone-\v{C}ech compactification and Gelfand transform, we discuss how any Dirichlet form defined on a measurable space can be transformed into a regular Dirichlet form on a locally compact space. T
Externí odkaz:
http://arxiv.org/abs/1212.1099