- Naotaka Kajino,

*The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the analytic aspects*.
January 20, 2020 version 1.0 pdf file (4.6MB) - Naotaka Kajino,

*The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the ergodic-theoretic aspects*.
January 6, 2020 version 1.0 - Naotaka Kajino and Mathav Murugan,
*On (non-)singularity of energy measures under full off-diagonal heat kernel estimates*.
October 7, 2019 version 1.0 pdf file (1.8MB) - Hiroshi Fujiwara, Naotaka Kajino and Yoshihiro Sawano,

*Laplace transform as Hilbert-Schmidt operators on reproducing kernel Hilbert spaces*.
June 16, 2010 version 1.0

January 29, 2020 version 1.1 pdf file (720KB)

August 6, 2010 version 1.1 pdf file (225KB)

- Naotaka Kajino, Equivalence of recurrence and Liouville property for symmetric Dirichlet forms,
- Alexander Grigor'yan and Naotaka Kajino, Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula,
- Sebastian Andres and Naotaka Kajino, Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions,
- Naotaka Kajino, Log-periodic asymptotic expansion of the spectral partition function for self-similar sets,
- Naotaka Kajino, Non-regularly varying and non-periodic oscillation of the on-diagonal heat kernels on self-similar fractals, in: Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics,
- Naotaka Kajino, Analysis and geometry of the measurable Riemannian structure on the Sierpiński gasket, in: Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I: Fractals in Pure Mathematics,
- Naotaka Kajino, On-diagonal oscillation of the heat kernels on post-critically finite self-similar fractals,
- Naotaka Kajino, Heat kernel asymptotics for the measurable Riemannian structure on the Sierpinski gasket,
- Naotaka Kajino, Time changes of local Dirichlet spaces by energy measures of harmonic functions,
- Naotaka Kajino, Remarks on non-diagonality conditions for Sierpinski carpets, in: Probabilistic Approach to Geometry,
- Naotaka Kajino, Spectral asymptotics for Laplacians on self-similar sets,

Preprint pdf file (123KB)

Preprint pdf file (541KB)

Preprint pdf file (254KB)

Preprint pdf file (958KB)

Preprint pdf file (2MB)

Preprint pdf file (1.7MB)

Preprint pdf file (1.8MB)

Preprint pdf file (958KB)

Preprint pdf file (414KB)

Preprint pdf file (635KB)

Preprint pdf file (770KB)