## Preprints

- Hiroshi Fujiwara, Naotaka Kajino and Yoshihiro Sawano,

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

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

## Refereed papers

- Naotaka Kajino, Equivalence of recurrence and Liouville property for symmetric Dirichlet forms,
*Matematicheskaya Fizika i Komp'yuternoe Modelirovanie (Mathematical Physics and Computer Simulation)* **2017, No. 3 (40)**, 89-98.

Preprint pdf file (123KB)
- Alexander Grigor'yan and Naotaka Kajino, Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula,
*Transactions of the American Mathematical Society* **369** (2017), 1025-1060.

Preprint pdf file (541KB)

- Sebastian Andres and Naotaka Kajino, Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions,
*Probability Theory and Related Fields* **166** (2016), 713-752. (The final publication is available at www.springerlink.com.)

Preprint pdf file (254KB)

- Naotaka Kajino, Log-periodic asymptotic expansion of the spectral partition function for self-similar sets,
*Communications in Mathematical Physics* **328** (2014), 1341-1370. (The final publication is available at www.springerlink.com.)

Preprint pdf file (958KB)

- 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,

*Contemporary Mathematics* **601**, 2013, pp. 165-194.

Preprint pdf file (2MB)

- 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,

*Contemporary Mathematics* **600**, 2013, pp. 91-133.

Preprint pdf file (1.7MB)

- Naotaka Kajino, On-diagonal oscillation of the heat kernels on post-critically finite self-similar fractals,
*Probability Theory and Related Fields* **156** (2013), 51-74. (The final publication is available at www.springerlink.com.)

Preprint pdf file (1.8MB)

- Naotaka Kajino,
Heat kernel asymptotics for the measurable Riemannian structure on the Sierpinski gasket,
*Potential Analysis* **36** (2012), 67-115. (The final publication is available at www.springerlink.com.)

Preprint pdf file (958KB)

- Naotaka Kajino,
Time changes of local Dirichlet spaces by energy measures of harmonic functions,
*Forum Mathematicum* **24** (2012), 339-363. (The final publication is available at www.degruyter.com.)

Preprint pdf file (414KB)

- Naotaka Kajino, Remarks on non-diagonality conditions for Sierpinski carpets,
in: Probabilistic Approach to Geometry,
*Advanced Studies in Pure Mathematics* **57**, 2010, pp. 231-241.

Preprint pdf file (635KB)

- Naotaka Kajino,
Spectral asymptotics for Laplacians on self-similar sets,
*Journal of Functional Analysis* **258** (2010), 1310-1360.

Preprint pdf file (770KB)