Hideyuki ISHI

Faculty of Science,
Osaka City University,
3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka 558-8585,


Japanese Page

Research Fields

Representation theory of Lie groups, Non-commutative harmonic analysis, Complex geometry, Mathematical Statistics

Works (Please contact me if you are interested in the papers below)

  1. An explicit description of positive Riesz distributions on homogeneous cones, Proc. Japan Acad. 74 (1998), 132--134.
  2. Representations of the solvable group acting on a homogeneous Siegel domain, Proc. Japan Acad. 75 (1999), 118--121.
  3. Representations of the affine transformation groups acting simply transitively on Siegel domains, J. Funct. Anal. 167 (1999), 425--462.
  4. Positive Riesz distributions on homogeneous cones, J. Math. Soc. Japan 52 (2000), 161--186.
  5. Basic relative invariants associated to homogeneous cones and applications, J. Lie Theory 11 (2001), 155--171.
  6. Determinant type differential operators on homogeneous Siegel domains, J. Funct. Anal. 183 (2001), 526--546.
  7. Decomposition of the $L^2$-function space on the Shilov boundary of a homogeneous Siegel domain, Sophia Kokyuroku in Mathematics 45 (2002), pp. 121--136.
  8. Unitarizability of holomorphically induced representations of a split solvable Lie group, in Proceedings of the ESI workshops 'Quantization and Analysis on Symmetric Spaces', pp. 96--100, 2005.
  9. The gradient maps associated to certain non-homogeneous cones, Proc. Japan Acad. 81 (2005), 44--46.
  10. Wavelet transforms for semidirect product groups with not necessarily commutative normal subgroups, J. Fourier Anal. Appl. 12 (2006), 37--52.
  11. On symplectic representations of normal $j$-algebras and their application to Xu's realizations of Siegel domains, Differential Geom. Appl. 24 (2006), 588--612.
  12. Matrix realizations of homogeneous Siegel domains, Proceedings of 'Workshop on Complex Geometry and Group Actions' pp. 79--85, 2007.
  13. (with T. Nomura) Tube domain and an orbit of a complex triangular group, Math. Z. 259 (2008), 697--711.
  14. (with T. Nomura) Irreducible homogeneous non-symmetric cones linearly isomorphic to the dual cones, in 'Contemporary geometry and topology and related topics', pp. 167--171, Cluj Univ. Press, 2008.
  15. A torus subgroup of the isotropy group of a bounded homogeneous domain, Manuscripta Math. 130 (2009), 353--358.
  16. (with T. Nomura) An irreducible homogeneous non-selfdual cone of arbitrary rank linearly isomorphic to the dual cone, in 'Infinite dimensional harmonic analysis IV', pp. 129--134, World Sci. Publ., 2009.
  17. (with C. Kai) The representative domains of a homogeneous bounded domain, Kyushu J. Math. 64 (2010), 35--47.
  18. Continuous wavelet transforms and non-commutative Fourier analysis, RIMS Kokyuroku Bessatsu B20 (2010), 173--185.
  19. (with S. Yamaji) Some estimates of the Bergman kernel of minimal bounded homogeneous domains, J. Lie Theory 21 (2011), 755--769.
  20. Unitary holomorphic multiplier representations over a homogeneous bounded domain, Adv. Pure Appl. Math. 2 (2011), no. 3-4, 405--419.
  21. Representation of clans and homogeneous cones, Vestnik Tambov University, 16 (2011), 1669--1675.
  22. (with A. J. Di Scala and A. Loi) Kaehler immersions of homogeneous Kaehler manifolds into complex space forms, Asian J. Math. 16 (2012), 479--488.
  23. The unitary representations parametrized by the Wallach set for a homogeneous bounded domain, Adv. Pure Appl. Math. 4 (2013), 93--102.
  24. On a class of homogeneous cones consisting of real symmetric matrices, Josai Mathematical Monograph 6 (2013), 71--80.
  25. (with P. Graczyk) Riesz measures and Wishart laws associated to quadratic maps, J. Math. Soc. Japan 66 (2014), 317--348.
  26. (with D. Bekolle and C. Nana) Koranyi's lemma for homogeneous Siegel domains of type II. Applications and extended results, Bull. Aust. Math. Soc. 90 (2014), 77--89.
  27. Orbit structure of the closure of a homogeneous cone, Comment. Math. Univ. St. Pauli 63 (2014), 105--115.
  28. Homogeneous cones and their applications to statistics, in `Modern methods of multivariate statistics', Travaux en Cours 82, pp. 135--154, Hermann, 2014.
  29. Matrix realization of a homogeneous cone, Lecture Notes in Comput. Sci. 9389, pp. 248--256, Springer, 2015.
  30. Explicit formula of Koszul-Vinberg characteristic functions for a wide class of regular convex cones, Entropy 18 (2016), Issue 11, 383; doi:10.3390/e18110383.
  31. (with T. Kogsio) Some properties of associated spaces with sub-Hankel determinants, Seminar on mathematical sciences 39, pp. 83--93, Keio University, 2016.
  32. (with J.-D. Park and A. Yamamori) Bergman kernel function for Hartogs domains over bounded homogeneous domains, J. Geom. Anal. 27 (2017), 1703--1736.
  33. (with P. Graczyk, S. Mamane and H. Ochiai) On the Letac-Massam Conjecture on cones $Q_{A_n}$, Proc. Japan Acad. Ser. A 93 (2017), 16--21.
  34. Matrix realization of a homogeneous Hessian domain, Lecture Notes in Comput. Sci. 10589, pp. 195--202, Springer, 2017.
  35. (with S. Gindikin) Cohomological Laplace transform on non-convex cones and Hardy spaces of dbar-cohomology on non-convex tube domains, J. Lie Theory 28 (2018), 245--263.
  36. (with A. Ohara) Doubly autoparallel structure on the probability simplex, Springer Proc. Math. Stat. 252, pp. 323--334, Springer, 2018.
  37. (with P. Graczyk and S. Mamane) Wishart exponential families on cones related to tridiagonal matrices, Ann. Inst. Stat. Math. 71 (2019), 439--471.
  38. (with E.Kurniadi) Harmonic analysis for 4-dimensional real Frobenius Lie algebras, Springer Proc. Math. Stat. 290 (2019), 95--109.
  39. (with B. Kolodziejek) Characterization of the Riesz exponential family on homogeneous cones, Colloq. Math. 158 (2019), no. 1, 45--57.
  40. (with P. Graczyk and B. Kolodziejek) Wishart laws and variance function on homogeneous cones, Probab. Math. Statist. 39 (2019), no. 2, 337--360.