Earlier Works

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Papers

Focusing on symmetry characterization theorems for homogeneous Siegel domains, Sugaku Expositions, 23 (2010), 47--67. PDF file 745Kb.
An irreducible homogeneous non-selfdual cone of arbitrary rank linearly isomorphic to the dual cone, joint work with H. Ishi, In "Infinite Dimensional Harmonic Analysis IV", J. Hilgert et al. (ed.), 129--134, World Scientific, Singapore, 2009.
Irreducible homogeneous non-symmetric cones linearly isomorphic to the dual cones, joint work with H. Ishi, In "Contemporary Geometry and Topology and Related Topics", D. Andrica and S. Moroianu (Ed.), Cluj Univ. Press, 2008, 167--171. PDF file 248Kb.
Tube domain and an orbit of a complex triangular group, joint work with H. Ishi, Math. Z., 259 (2008), 697--711. MR2395134, Document, PDF: 32M10 (32A07). Zbl 1143.22005: *22E25, 22-06.
On a certain 8-dimensional non-symmetric homogeneous convex cone, In "Quantization and Analysis on Symmetric Spaces (H. Upmeier Ed.)" , ESI preprint 1793 (2006), 70--73.
A characterization of symmetric tube domains by convexity of Cayley transform images, joint work with C. Kai, Diff. Geom. Appl., 23 (2005), 38--54. MR2148909 (2006b:32028) , Document, PDF: 32M15 (43A85). Zbl 1075.43008: *43A85, 32M10, 32M15.
A characterization of symmetric cones through pseudoinverse maps, joint work with C. Kai, J. Math. Soc. Japan, 57 (2005), 195--215. MR2114729 (2006a:32027) , Document, PDF: 32M15 (22E30 43A85). Zbl 1086.32021: *32M15, 22E30, 43A85.
Geometric norm equality related to the harmonicity of the Poisson kernel for homogeneous Siegel domains, J. Funct. Anal., 198 (2003), 229--267. MR 2004a:32033, Document, PDF: 32M15. Zbl 1026.32046: *32M15, 32M05, 32M10, 32W99.
Family of Cayley transforms of a homogeneous Siegel domain parametrized by admissible linear forms, Diff. Geom. Appl., 18 (2003), 55--78. MR 2004c:32048, Document, PDF: 32M10 (43A85). Zbl 1023.22007: *22E25, 32M10.
Cayley transforms and symmetry conditions for homogeneous Siegel domains, Adv. Stud. Pure Math., 37 (2002), 253--265. MR 2004e:32026, Document, PDF: 32M15 (32M10). Zbl 1035.32015: *32M99.
A symmetry characterization for homogeneous Siegel domains related to Berezin transforms, In "Geometry and analysis on finite- and infinite-dimensional Lie groups", A. Strasburger et al. ed., Banach Center Publ., 55 (2002), 323--334; Proceedings of the workshop "Lie groups and Lie algebras", Bedlewo (Poland), Sep. 04--15, 2000; MR 2003h:32037, Document, PDF: 32M15 (43A85). Zbl 1010.22013: *22E30, 32M15, 43A85.
A characterization of symmetric Siegel domains through a Cayley transform, Transform. Groups, 6 (2001), 227--260. MR 2002k:32042, Document, PDF: 32M15. Zbl 1015.32019: *32M15, 44A05.
Berezin transforms and Laplace-Beltrami operators on homogeneous Siegel domains, Diff. Geom. Appl., 15-1 (2001), 91--106. MR 2002g:32048, Document, PDF: 32W50 (32M10 43A85). Zbl 990.22007: *22E30, 43A85, 32M10.
On Penney's Cayley transform of a homogeneous Siegel domain, J. Lie Theory, 11 (2001), 185--206. MR 2002c:32035, Document, PDF: 32M15 (32A50). Zbl 977.32015: *32M15.
Spherical Fourier transforms of the Berezin kernels on symmetric Siegel domains,Unpublished manuscript (with H. Ishi).
Invariant Berezin transforms, in "Harmonic analysis and integral geometry" (Proc. Summer Univ. held at Safi, Morocco), Edited by M. Picardello, Chapman & Hall/CRC Research Notes in Math., 422 (2001), 19--40. MR 2001m:22019, Document, PDF: 22E30 (32A50 43A75 43A85). Zbl 976.22007: *22E30, 43A85, 33C80, 43A75.
Berezin transforms and group representations,J. Lie Theory, 8 (1998), 433-440. MR 2000c:22003, Document, PDF: 22D10 (22E27, 32A36, 46E22, 47A67), Zbl 919.43008: *43A85, 32M15, 47N50..
Berezin transforms on the $2 \times 2$ matrix space related to the $U(2) \times U(2)$-action, Integral Equations Operator Theory, 32 (1998), 152-179 (with E. Fujita). MR 99k:43008, Document, PDF: 43A80 (32M15, 33C45, 47A10, 47B38), Zbl 910.43008: *43A80, 22E70, 47G10, 47B38, 47A75, 33C45.
Unifying two beta-integrals, Unpublished manuscript, 1997.
Spectral decompositions of Berezin transformations on $\mathbf{C}^n$ related to the natural $U(n)$-action, J. Math. Kyoto Univ., 36 (1996), 877-888 (with E. Fujita). MR 98e:47048, Document, PDF: 47B38 (22E45, 32M15, 46N50, 47G10, 47N50), Zbl 910.43006: *43-99, 47-99.
Grassmann manifold of a $JH$-algebra, Ann. Global Anal. Geom., 12 (1994), 237-260. MR 95h:58006, Document, PDF: 58B20 (17C65, 46H70, 46K70), Zbl 829.46040: *46H70, 17C27, 58B20.
Une nouvelle démonstration des identités de Hecke, Kyoto-Math. Preprint, 93-09 (1993), DVI file, PDF file.
Manifold of primitive idempotents in a Jordan-Hilbert algebra, J. Math. Soc. Japan, 45 (1993), 37-58. MR 94a:58010, Document, PDF: 58B20 (17C65, 46K70), Zbl 791.58011: *58B20, 17C27.
Algebraically independent generators of invariant differential operators on a bounded symmetric domain, J. Math. Kyoto Univ., 31 (1991), 265-279. MR 92c:32040, Document, PDF: 32M15 (17C65, 46L70), Zbl 746.32011: *32M15, 43A85, 17C30.
Algebraically independent generators of invariant differential operators on a symmetric cone, J. Reine Angew. Math., 400 (1989), 122-133. MR 91h:22021, Document, PDF: 22E30 (17C30), Zbl 667.43007: *43A85, 53C35, 17C10, 58G30.
A description of a space of holomorphic discrete series by means of the Fourier transform on the \v Silov boundary, J. Funct. Anal., 82 (1989), 1-37. MR 90g:22023, Document, PDF: 22E46 (32M15, 43A85, 46E99, 46J15), Zbl 681.46045: *46G20, 46J20.
Harmonic analysis on a nilpotent Lie group and representations of a solvable Lie group on $\overline{\partial}_b$ cohomology spaces, Japan. J. Math., 13 (1987), 277-332. MR 89f:22014, Document, PDF: 22E27 (22E45, 32M05, 32M10), Zbl 646.22005: *22E27, 32M10, 43A85, 22E30.
Existence of a non-inductive linear form on certain solvable Lie algebras, J. Math. Soc. Japan, 39 (1987), 667-675. MR 89a:17014, Document, PDF: 17B30, Zbl 661.17009: *17B30, 22E27, 17B20, 17B45.
Representations of a solvable Lie group on $\overline{\partial}_b$ cohomology spaces, Proc. Japan Acad., 62 (1986), 331-334. MR 88f:22036, Document, PDF: 22E45 (22E27, 32C35), Zbl 626.22005: *22E27, 22E30, 32M15, 43A85.
Fourier transform of a space of holomorphic discrete series, Proc. Japan Acad., 61 (1985), 133-136. MR 87g:22019, Document, PDF: 22E46 (22E30), Zbl 611.43003: *43A80, 32A07, 22E30.
The Paley-Wiener type theorem for the oscillator group, J. Math. Kyoto Univ., 22 (1982), 71-96. MR 85k:22024, Document, PDF: 22E30 (33A75, 43A65), Zbl 529.43006: *43A80, 22E30, 43A30.
Harmonic analysis on the universal covering group of certain semidirect product Lie group, Japan. J. Math., 6 (1980), 129-145. MR 82i:22015, Document, PDF: 22E30 (43A80), Zbl 461.43015: *43A80, 43A30, 22E30.
The Paley-Wiener type theorem for finite covering groups of $SU(1,1)$, J. Math. Kyoto Univ., 18 (1978), 273-304. MR 58 #11224, Document, PDF: 22E30, Zbl 406.43005: *43A80, 43A30, 22E30.
The Paley-Wiener type theorem for finite covering groups of $SU(1,1)$, Proc. Japan Acad., 53 (1977), 195-197. MR 58 #1012, Document, PDF: 22E30, Zbl 406.43006: *43A80, 43A30.

Slides in English

Analysis and geometry related to homogeneous Siegel domains and homogeneous convex cones, PDF file. part I 289Kb, part II 259Kb, for talks in Lie transformation groups and complex geometry (September 27, 28, 2010) at Yuzawa, Niigata.
Right multiplication operators in the clan structure of a Euclidean Jordan algebra, PDF file 278Kb, for talks in Harmonic analysis and representations of Lie groups (April 22, 2009) at Tambov University.
Symmetry characterization theorems for homogeneous convex cones and Siegel domains, PDF file. part I 288Kb, part II 307Kb, part III 294Kb, for talks in Harmonic analysis and partial differential equations (April 1, 2, 4, 2009) at Cadi Ayyad University, Marrakech.
Homogeneous Siegel domains --- Analysis and Geometry, PDF file 199Kb, for talk in "The 3rd PKNU-KU Joint Symposium" at Pukyong Univ. (November 30, 2007).
Focusing on symmetry characterization theorems for homogeneous Siegel domains, PDF file 424Kb, for talks in Complex analysis, operator theory and applications to mathematical physics (September 23, 2005) at the Erwin Schrödinger International Institute for Mathematical Physics, and at Mainz University (March 16, 2006).

Cayley transforms of a homogeneous Siegel domain, PDF file 366Kb, for talks at Scuola Normale Superiore di Pisa (March 09, 2006), in Workshop on Jordan structures in analysis and geometry at National Sun Yat-sen Univ. (April 06, 2006), and at Tambov Univ. (September 28, 2006).

Tube domain and an orbit of a complex triangular group, PDF file 296Kb, for talks at Tukuba Conference on Integral Geometry and Harmonic Analysis (August 08, 2006), at Tambov Univ. (September 26, 2006), and at Sfax Univ. (November 22, 2006).

Some symmetry conditions of homogeneous Siegel domains, PDF file 119Kb, for talk in Oberseminar Geometrie, Topologie und Analysis at Univ. Köln, January 30, 2004.

Symmetry of homogeneous Siegel domains and harmonicity of the Poisson-Hua kernel, PDF file 114Kb, for talk in the the conference "Analysis and Probability Related to Solvable Lie Groups", Zakopane, Poland, 15 -- 22 June, 2002.

Symmetry characterizations for homogeneous Siegel domains related to Laplace-Beltrami operators, PDF file 846Kb, for talk in the workshop "Representation Theory of Lie Groups", RIMS, 18 -- 22 February, 2002.

Geometric norm equality related to the harmonicity of the Poisson-Hua kernel for homogeneous Siegel domains, PDF file 303Kb, for talk in the 2001 Twente Conference on Lie Groups at Twente University, the Netherlands, 17 -- 19 December, 2001.

Geometric connection of the Poisson kernel with a Cayley transform for homogeneous Siegel domains, PDF file 303Kb, for talk in the Workshop "Integral Geometry in Representation Theory" at MSRI, 08 -- 12 October, 2001.

Short abstracts in English

Two characerizations of symmetric Siegel domains by the Laplace-Beltrami operator and their geometric backgrounds, DVI file 6.9Kb. Abstract for NUS-JSPS Workshop on Algebra at National University of Singapore, Singapore, 09 -- 13 July, 2001.
Symmetry conditions for homogeneous Siegel domains and their applications, PS file 50Kb (from the conference site); DVI file 2Kb (from here). Abstract for "Real and Complex Harmonic Analysis Related to Homogeneous Manifolds" at Zakopane, Poland, 11 -- 19 January, 2001.
Berezin transforms and Laplace-Beltrami operators on homogeneous Siegel domains --- commutativity, symmetry of the domain and a Cayley transform ---, talk at the "International Conference on Lie Groups, Geometric Structures and Differential Equations --- One Hundred Years after Sophus Lie ---" at RIMS on Dec. 16, 1999, DVI file.
Berezin transforms related to multiplicity free actions, Oberwolfach Conference "Harmonische Analyse und Darstellungstheorie topologischer Gruppen", 04.05 -- 10.05.1997, Tagungsbericht, 18/1997, 7: DVI file.
Grassmann manifold of a Hilbert Jordan algebra, CIRM Conference "Représentations des Groupes et Analyse Complexe", 30 août -- 03 Septembre, 1993, DVI file.
Unitary representations of a solvable Lie group on $\overline{\partial}_b$ cohomology spaces, Oberwolfach Conference "Harmonische Analyse und Darstellungstheorie topologischer Gruppen", 28.06 -- 04.07.1987, Tagungsbericht, 28/1987, 17.

List of my articles in RIMS Kôkyûroku etc. (in Japanese)

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