Preprints

• Naotaka Kajino and Mathav Murugan,
  Heat kernel estimates for boundary trace of reflected diffusions on uniform domains.
  December 14, 2023 version 0.9 pdf file (724KB)
• Naotaka Kajino and Ryosuke Shimizu,
  p-Energy forms on fractals: recent progress.
  December 14, 2023 version 1.0
• 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, An elementary proof that walk dimension is greater than two for Brownian motion on Sierpiński carpets,
  Bulletin of the London Mathematical Society 55 (2023), 508-521.
  Preprint pdf file (942KB)
• Naotaka Kajino and Mathav Murugan,
  On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions,
  Inventiones mathematicae 231 (2023), 263-405.
• Naotaka Kajino,
  On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates II: Some borderline examples,
  in: Dirichlet Forms and Related Topics: In Honor of Masatoshi Fukushima's Beiju, IWDFRT 2022, Osaka, Japan, August 22-26,
  Springer Proceedings in Mathematics & Statistics 394, 2022, pp. 223-251.
  
• Naotaka Kajino,
  The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the analytic aspects,
  in: Stochastic Analysis, Random Fields and Integrable Probability ― Fukuoka 2019,
  Advanced Studies in Pure Mathematics 87, 2021, pp. 293-314.
  Preprint pdf file (4.6MB)
• Naotaka Kajino and Mathav Murugan,
  On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates,
  The Annals of Probability 48 (2020), 2920-2951.
  Preprint pdf file (1.8MB)
• 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)

Other published articles (not refereed)

• Naotaka Kajino,
  The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the ergodic-theoretic aspects,
  RIMS Kôkyûroku 2176 (2021), 111-119.
  Preprint pdf file (720KB)
• Naotaka Kajino, Energy measures for diffusions on fractals: a survey,
  in: Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs,
  Advances in Analysis and Geometry 3, 2021, pp. 119-142.