Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Kajino, Naotaka"'
Autor:
Kajino, Naotaka, Shimizu, Ryosuke
We introduce new contraction properties called the generalized $p$-contraction property for $p$-energy forms as generalizations of many well-known inequalities, such as Clarkson's inequalities, the strong subadditivity and the ``Markov property'' in
Externí odkaz:
http://arxiv.org/abs/2404.13668
Autor:
Kajino, Naotaka, Shimizu, Ryosuke
We construct good $p$-energy forms on metric measure spaces as pointwise subsequential limits of Besov-type $p$-energy functionals under certain geometric/analytic conditions. Such forms are often called Korevaar-Schoen $p$-energy forms in the litera
Externí odkaz:
http://arxiv.org/abs/2404.13435
Autor:
Kajino, Naotaka, Murugan, Mathav
We study the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat kernel esti
Externí odkaz:
http://arxiv.org/abs/2312.08546
Autor:
Kajino, Naotaka
We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular Sierpi\'{n}ski gaskets and each of which is equipped with a canonical strongly local regular symmetric Dirichlet form. We prove that any fractal $K$ in
Externí odkaz:
http://arxiv.org/abs/2108.02027
We study the directed polymers in random environment on an infinite graph $G=(V,E)$ on which the underlying random walk satisfies sub-Gaussian heat kernel bounds with spectral dimension $d_{s}$ strictly less than two. Our goal in this paper is to sho
Externí odkaz:
http://arxiv.org/abs/2010.12312
Autor:
Kajino, Naotaka, Murugan, Mathav
We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact that, for a given strongly local, regular symmetric Dirichlet space in
Externí odkaz:
http://arxiv.org/abs/2008.12836
Autor:
Kajino, Naotaka
We give an elementary self-contained proof of the fact that the walk dimension of the Brownian motion on an arbitrary generalized Sierpi\'{n}ski carpet is greater than two, no proof of which in this generality had been available in the literature. Ou
Externí odkaz:
http://arxiv.org/abs/2005.02524
Autor:
Kajino, Naotaka
This short survey is aimed at sketching the ergodic-theoretic aspects of the author's recent studies on Weyl's eigenvalue asymptotics for a \emph{"geometrically canonical" Laplacian} defined by the author on some self-conformal circle packing fractal
Externí odkaz:
http://arxiv.org/abs/2001.11354
Autor:
Kajino, Naotaka
This article surveys the analytic aspects of the author's recent studies on the construction and analysis of a "geometrically canonical" Laplacian on circle packing fractals invariant with respect to certain Kleinian groups (i.e., discrete groups of
Externí odkaz:
http://arxiv.org/abs/2001.07010
Autor:
Kajino, Naotaka, Murugan, Mathav
We show that for a strongly local, regular symmetric Dirichlet form over a complete, locally compact geodesic metric space, full off-diagonal heat kernel estimates with walk dimension strictly larger than two (\emph{sub-Gaussian} estimates) imply the
Externí odkaz:
http://arxiv.org/abs/1910.02601