Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Kelleher, Daniel J."'
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
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
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
Autor:
Ignatowich, Michael J., Kelleher, Daniel J., Maloney, Catherine E., Miller, David J., Nechyporenko, Khrystyna
Much is known in the analysis of a finitely ramified self-similar fractal when the fractal has a harmonic structure: a Dirichlet form which respects the self-similarity of a fractal. What is still an open question is when such structure exists in gen
Externí odkaz:
http://arxiv.org/abs/1204.5815
The brain is one of the most studied and highly complex systems in the biological world. It is the information center behind all vertebrate and most invertebrate life, and thus has become a major focus in current research. While many of these studies
Externí odkaz:
http://arxiv.org/abs/1109.3888
Autor:
Begue, Matthew, Kelleher, Daniel J., Nelson, Aaron, Panzo, Hugo, Pellico, Ryan, Teplyaev, Alexander
We investigate the relation between simple random walks on repeated barycentric subdivisions of a triangle and a self-similar fractal, Strichartz hexacarpet, which we introduce. We explore a graph approximation to the hexacarpet in order to establish
Externí odkaz:
http://arxiv.org/abs/1106.5567