Preprints

• Naotaka Kajino and Ryoichiro Noda,
  Generalized Kac's moment formula for positive continuous additive functionals of symmetric Markov processes.
  March 6, 2025 version 1.0
  March 13, 2025 version 2.0 pdf file (130KB)
• Naotaka Kajino and Ryosuke Shimizu,
  Contraction properties and differentiability of p-energy forms with applications to nonlinear potential theory on self-similar sets.
  April 21, 2024 version 0.8
  September 28, 2024 version 0.9 pdf file (7.9MB)
  January 20, 2025 version 1.0 pdf file (8MB)
• Naotaka Kajino and Ryosuke Shimizu,
  Korevaar--Schoen p-energy forms and associated p-energy measures on fractals.
  April 20, 2024 version 1.0
  September 29, 2024 version 2.0 pdf file (3.3MB)
• Naotaka Kajino and Mathav Murugan,
  Heat kernel estimates for boundary traces of reflected diffusions on uniform domains.
  December 14, 2023 version 0.9
  July 19, 2024 version 1.0
  February 21, 2025 version 2.0 pdf file (1MB)
• Naotaka Kajino and Ryosuke Shimizu,
  p-Energy forms on fractals: recent progress.
  December 14, 2023 version 1.0 pdf file (409KB)
• 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.