Japanese version || Kyoto University > Graduate School of Science > Department of Mathematics > Probability Theory > Ichiro SHIGEKAWA |

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**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):- 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) - 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) - 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) - L^p contraction semigroups for vector valued functions,
J. Funct. Anal.,
**147**(1997), 69-108.

(DVI file 143Kb) - 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)
- A non-symmetric diffusion process on the Wiener space

(DVI file 63Kb) - Semigroup domination on a Riemannian manifold with boundary,
Acta Applicandae Math.,
**63**(2000), 385-410.

(DVI file 103Kb) (PDF file ) - 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) - 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) - 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) - 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) - 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 - 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 - 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) - Schr\"odinger operators on the Wiener space,
Communications on Stochastic Analysis,
**1**(2007), 1-17

(DVI file 71Kb) (PDF file 166Kb) - Generalized entropy, fractional logarithmic Sobolev inequality,
and Beckner type inequality (with Qing-Ping Liu),

(DVI file 108Kb) (PDF file 199Kb) - Witten Laplacian on a lattice spin system,

AstÃ©risque No. 327 (2009), 115-129. (PDF file 155Kb) - 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) - Semigroups preserving a convex set in a Banach space,

Kyoto Journal of Mathematics,**51**no. 3, (2011), 647-672.

(PDF file **Kb) -> - 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 - Exponential convergence of Markovian semigroups and their spectra
on
*L*-spaces (with Seiichiro Kusuoka),^{p}

Kyoto Journal of Mathmatics,**54**, No. 2, (2014) 367-399, (PDF file 222Kb) - 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) - Ultracontractivity for non-symmetric Markovian semigroups,

"*Festschrift Masatoshi Fukushima*," pp. 527-551, Interdisiplinary Mathmetical Sciences, World Scientific, 2015 (PDF file 187Kb)

- Dirichlet forms on separable metric spaces
(with Setsuo Taniguchi),
"
**List of Publication in MathSciNet**

- 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.

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/ |