activity
20152025
most citedThe Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the ergodic-theoretic aspects

2 citations · 2 across the 6 of their papers we have counts for

collaborators

10 papers

math.PR2025

Two-sided heat kernel bounds for -Liouville Brownian motion

Sebastian Andres, Naotaka Kajino, Konstantinos Kavvadias +1

Liouville Brownian motion (LBM) is the canonical diffusion process on a Liouville quantum gravity (LQG) surface. In this work, we establish upper and lower bounds for the heat kern…

math.PR2025

Generalized Kac's moment formula for positive continuous additive functionals of Markov processes

Naotaka Kajino, Ryoichiro Noda

We establish a formula for moments of certain random variables involving positive continuous additive functionals (PCAFs) of standard processes which have absolutely continuous tra…

math.FA2025

-Energy forms on fractals: recent progress

Naotaka Kajino, Ryosuke Shimizu

In this article, we survey recent progress on self-similar -energy forms on self-similar fractals, where . While for the notion of such forms coincides wit…

math.FA2024

Contraction properties and differentiability of -energy forms with applications to nonlinear potential theory on self-similar sets

Naotaka Kajino, Ryosuke Shimizu

We introduce a new contraction property, which we call the generalized -contraction property, for -energy forms as generalizations of many well-known inequalities, such as $p…

math.FA2024

Korevaar-Schoen -energy forms and associated -energy measures on fractals

Naotaka Kajino, Ryosuke Shimizu

We construct good -energy forms on metric measure spaces as pointwise subsequential limits of Besov-type -energy functionals under certain geometric/analytic conditions. Such…

math.PR2021

On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates II: Some borderline examples

Naotaka Kajino

We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular Sierpiński gaskets and each of which is equipped with a canonical strongly local…