Ichiro SHIGEKAWA

• Major Field: Probability theory
• Interests: stochasic analysis, Malliavin calculus, Dirichlet forms on infinite dimensional spaces, stochasic analysis on path/loop spaces
• Preprints (already published papers included):
  1. Dirichlet forms on separable metric spaces (with Setsuo Taniguchi), "Probability theory and mathematical statistics," (Kiev, 1991), 324-353, World Sci. Publ., River Edge, NJ, 1992.
     (PDF file)
  2. A K\"ahler metric on a based loop group and a covariant differentiation (with Setsuo Taniguchi), in "It\^o's stochastic calculus and probability theory," ed. by N. Ikeda et al, pp. 327-346, Springer-Verlag, Berlin-Heidelberg-New York, 1996.
     (DVI file 95Kb) (PostScript file) (PDF file)
  3. Differential calculus on a based loop group, in "New Trends in Stochastic Analysis," Proceedings of the Taniguchi International Symposium, ed. by K. Elworthy, S. Kusuoka and I. Shigekawa, pp. 375-398, World Scientific, Singapore, 1997.
     (DVI file 81Kb) (PostScript file) (PDF file)
  4. L^p contraction semigroups for vector valued functions, J. Funct. Anal., 147 (1997), 69-108.
     (DVI file 143Kb)
  5. The Meyer inequality for the Ornstein-Uhlenbeck operator in L^1 and probabilistic proof of Stein's L^p multiplier theorem, Proceedings of SAP '96, "Tends in probability and related analysis," ed. by N. Kono and N.-R. Shieh, World Scientific, pp. 273-288, Singapore, 1997.
     
  (DVI file 51Kb)
  6. A non-symmetric diffusion process on the Wiener space
     (DVI file 63Kb)
  7. Semigroup domination on a Riemannian manifold with boundary, Acta Applicandae Math., 63 (2000), 385-410.
     (DVI file 103Kb) (PDF file )
  8. The domain of a generator and the intertwining property in "Stochastics in Finite and Infinite Dimensions" ed. by T. Hida et al, pp. 401-410, Birkh\"auser, Boston, 2001.
     (DVI file 34Kb)
  9. Littlewood-Paley inequality for a diffusion satisfying the logarithmic Sobolev inequality and for the Brownian motion on a Riemannian manifold with boundary, Osaka J. Math., 39 (2002), 897-930.
     (DVI file 143Kb) (PDF file 248Kb)
  10. Vanishing theorem of the Hodge-Kodaira operator for differential forms on a convex domain of the Wiener space, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6 (2003), 53-63.
      (DVI file 39Kb) (PDF file 109Kb)
  11. Orlicz norm equivalence for the Ornstein-Uhlenbeck operator
      in "Stochastic analysis and related topics in Kyoto," pp. 301-317, Adv. Stud. Pure Math., 41, Math. Soc. Japan, Tokyo, 2004.
      (DVI file 60Kb) (PDF file 155Kb)
  12. L^p multiplier theorem for the Hodge-Kodaira operator, "Seminaire de Probabilite XXXVIII," Lecture Notes in Math. vol. 1857, pp. 226-246, Springer, Berlin-Heidelberg-New York, 2005
      (DVI file 90Kb) (PDF file 184Kb) -> Direct link to Springer
  13. On equivalence of $L^p$-norms related to Schr\"odinger type operators on Riemannian manifolds (with Tomohiro Miyokawa), Probability Theory and Related Fields, 135 (2006), 487-519.
      (DVI file 143Kb) (PDF file 219Kb) -> Direct link to Probability Theory and Related Fields
  14. Defective intertwining property and generator domain, Journal of Functional Analysis, 239 (2006), 357-374.
      (DVI file 60Kb) (PDF file 149Kb) -> Direct link to The digital object identifier (DOI)
  15. Schr\"odinger operators on the Wiener space, Communications on Stochastic Analysis, 1 (2007), 1-17
      (DVI file 71Kb) (PDF file 166Kb)
  16. Generalized entropy, fractional logarithmic Sobolev inequality, and Beckner type inequality (with Qing-Ping Liu),
      (DVI file 108Kb) (PDF file 199Kb)
  17. Witten Laplacian on a lattice spin system,
      Astérisque No. 327 (2009), 115-129. (PDF file 155Kb)
  18. Non-symmetric diffusions on a Riemannian manifold,
      Probabilistic approach to geometry, pp. 437-461, Adv. Stud. Pure Math., 57, Math. Soc. Japan, Tokyo, 2010. (PDF file 199Kb)
  19. Semigroups preserving a convex set in a Banach space,
      Kyoto Journal of Mathematics, 51 no. 3, (2011), 647-672.
      (PDF file **Kb) ->
  20. On spectra of 1-dimensional diffusion operators,
      Mathematical Quantum Field Theory and Related Topics, RIMS Kokyuroku No. 1859, (2013), 59-75. -> Direct link to RIMS Kokyuroku
  21. Exponential convergence of Markovian semigroups and their spectra on L^p-spaces (with Seiichiro Kusuoka),
      Kyoto Journal of Mathmatics, 54, No. 2, (2014) 367-399, (PDF file 222Kb)
  22. Dual ultracontractivity and its applications,
      Frontiers of Mathematics in China, 9, No. 9, (2014), 899-928
      DOI: 10.1007/s11464-014-0398-y (PDF file 187Kb)
  23. Ultracontractivity for non-symmetric Markovian semigroups,
      "Festschrift Masatoshi Fukushima," pp. 527-551, Interdisiplinary Mathmetical Sciences, World Scientific, 2015 (PDF file 187Kb)
• List of Publication in MathSciNet

Books

• Ichiro Shigekawa: Stochastic Analysis, American Mathematical Society, 2004
  
• Kiyosi Ito: Poisson Point Processes and Their Application to Markov Processes , SpringerBriefs in Probability and Mathematical Statistics, Editors: Shinzo Watanabe and Ichiro Shigekawa, Springer, 2015.
  

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Ichiro SHIGEKAWA

TEL: 075-753-3729

FAX: 075-753-3711

E-MAIL: ichiro math.kyoto-u.ac.j

URL: http://www.math.kyoto-u.ac.jp/~ichiro/

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