論文

リス ト2022 年 3 月 29 日
古谷 賢朗

email:furutani kenro[at]ma.noda.tus.ac.jp(A) 査 読 付 き(1) Kurando Baba, Kenro Furutani, Calabi-Yau structure and Bargmann type transformation on the Cayley projective plane, Advance publication (March 2022)
in the Journal of the Mathematical Society of Japan.
(2) Kenro Furutani, Irina Markina, Automorphism groups of pseudo H-type algebras, Journal of Algebra, 568(2021), 91–138 (Available online 16 October2020).
(3) Kenro Furutani, Residue of the spectral zeta function of a sub-Laplacian ona certain class of nilmanifolds, Applied Analysis and Optimization, 4(2020),no.1, 51–64.
(4) Wolfram Bauer, Kenro Furutani, Chisato Iwasaki and Abdellah Laaroussi, Spectral theory of a class of nilmanifolds attached to Cliﬀord modules, Mathematische Zeitschrift, published online 03 April 2020.
(5) Kenro Furutani, Irina Markina, Complete classification of pseudo H-type algebras:II, Geometriae Dedicata, 202(2019), 233–264.
(6) Kenro Furutani, Mitsuji Tamura, Riemann submersion and Maslov quantization condition, Applied Analysis and Optimization, 2, No. 3(2018), 373–401.
(7) Kenro Furutani, Irina Markina, Mauricio Godoy Molina, Tohru Morimoto andAlexander Vasiliev, Lie algebras attached to Cliﬀord modules and simple graded
Lie algebras, J. Lie Theory, Vol. 28, no. 3(2018), 843–864.
(8) Christian Autenried, Kenro Furutani, Irina Markina, and Alesander Vasiliev,
Pseudo metric 2-step nilpotent Lie algebras, Advances in Geometry, 18(2018),
No. 2, 237–263.
(9) Kenro Furutani, Mitsuji Tamura, Double submersions and Hamilton flows, Applied Analysis and Optimization, 1, no. 3(2017), 381–400.
(10) Wolfram Bauer, Kenro Furutani and Mitsuji Tamura, First integrals of bicharacteristic curves of a sub-Laplacian and related Grushin type operators,Journal of Non-linear and Convex Analysis, 18, no. 5(2017), 893–917.
(11) Wolfram Bauer and K. Furutani and Chisato Iwasaki, Sub-Riemannian structures in a principal bundle and their Popp measures, 96(2017), no. 14, 2390–2407, published online on 02/June/2017 in Applicable Analysis.
12(12) Wolfram Bauer and Kenro Furutani and Chisato Iwasaki, A codimension 3 subRiemannian structure on Gromoll-Meyer exotic sphere, Diﬀerential Geometry
and its Applications, 53(2017), 114–136.
(13) Kenro Furutani, Irina Markina, Complete classification of pseudo H-type algebras:I, Geometriae Dedicata, 190(2017), 23–51.
(14) Kenro Furutani and Mitsuji Tamura, Submersion and bi-characteristic curvesof Grushin type operators, Journal of Non-linear and Convex Analysis, 17(2016),
no. 9, 1697–1716.
(15) Kenro Furutani, Irina Markina and Alexander Vasiliev, Free nilpotent and Htype Lie algebras. Combinatorial and orthogonal designs, Journal of pure andapplied algebra, 219(2015), 5467–5492.
(16) Wolfram Bauer and Kenro Furutani and Chisato Iwasaki, Spectral zeta function
on pseudo H-type nilmanifolds, Indean Journal of Pure and Applied Mathematics, 46(2015), no. 4, 539–582.
(17) Wolfram Bauer and Kenro Furutani and Chisato Iwasaki, The inverse of a parameter family of degenerate operators and applications to the Kohn-Laplacian,Advances in Mathematics, 277(2015), 283–337.
(18) Wolfram Bauer and Kenro Furutani and Chisato Iwasaki, Fundamental solution of a higher step Grushin type operator, Advances in Mathematics, Vol.
271(2015), 188–234.
(19) Kenro Furutani and Irina Markina, Existence of the lattice on general H-typegroups, Journal of Lie Theory, 24(2014), no. 4, 979–1011.
(20) Wolfram Bauer and Kenro Furutani and Chisato Iwasaki, Trivializable subRiemannian structures on spheres, Journal : Bulletin des Sciences Mathématiques,137(2013), 361–385.
(21) Kenro Furutani, Chisato Iwasaki and Toshinao Kagawa, An action function fora higher step Grushin operator, Journal of Geometry and Physics, 62(2012),1949–1976.
(22) Wolfram Bauer and Kenro Furutani and Chisato Iwasaki, Spectral zeta functionof the sub-Laplacian on two step nilmanifolds, Journal de Mathématiques pures
et appliquées, 97(2012), 242–261.
(23) Wolfram Bauer and Kenro Furutani, Spectral zeta function of a sub-Laplacian
on product sub-Riemannian manifolds and zeta-regularized determinant, Journal of Geometry and Physics, 60(2010), 1209–1234.
(24) Wolfram Bauer and Kenro Furutani and Chisato Iwasaki, Spectral Analysis
and Geometry of a sub-Laplacian and related Grushin type operators, Trends
in partial Diﬀerential Equations and Spectral Theory in ”Advances in Partial
Diﬀerential Equations”, 211, 183–290(2010), Birkhäuser.
(25) Wolfram Bauer and Kenro Furutani, Spectral Analysis and Geometry of a SubRiemannian Structure on S 3 and S 7 , Journal of Geometry and Physics,58, No.
12(2008), 1693–1738.
(26) Wolfram Bauer, Kenro Furutani, Quantization operators on Quadrics, Kyushu
Journal of Mathematics, Vol.62, No. 1(2008), 221–258.

3(27) Wolfram Bauer, Kenro Furutani, Zeta-regularized Determinant of the Laplacian for classes of spherical space forms, Journal of Geometry and Physics,
Vol. 58(2008), 64–88.
(28) Wolfram Bauer, Kenro Furutani, Compact Operators and the Pluriharmonic
Berezin Transform, International Journal of Mathematics, Vol.19, No. 6(2008),645–669.
(29) Wolfram Bauer, Kenro Furutani, Hilbert-Schmidt Hankel Operstors and Berezin
Iterations, Tokyo Journal of Mathematics, Vol. 31, No. 2, 293–319 (2008).
(30) Kenro Furutani, Heat kernels of the sub-Laplacian and Laplacian on nilpotent
Lie groups, Analysis, Geometry and Topology of Elliptic Operators, papers
in honour of Krzysztof P. Wojciechowsky, pp.185–226 (2006)(World Scientific,London-Singapore).
(31) Kenro Furutani, Pseudo-diﬀerential operator and Reproducing kernels arrisingin Geometric quantization, Operator theory : Advances and Application(Birkhäuserverlag) Vol. 164, pp. 133–151 (2006).
(32) Kenro Furutani, Atiyah-Patodi-Singer boundary condition and a splitting formula of a spectral flow, Journal of Geometry and Physics, Vol. 56, No. 2(2006),
pp. 310–321.
(33) Kenro Furutani, Fredholm-Lagrangian-Grassmannian and the Maslov index,
Journal of Geometry and Physics、Vol. 51, No. 3(2004), pp. 269–331.
(34) Kenro Furutani, On the Quillen determinant, Journal of Geometry and Physics,
Vol. 49, No. 3-4, pp. 366-375 (2004).
(35) Kenro Furutani and Serge de Gosson, Determinant of Laplacians on Heisenberg
Manifolds, Journal of Geometry and Physics, Vol. 48, No. 2-3, pp. 438-479(2003).
(36) Kenro Furutani, A Kähler structure on the punctured cotangent bundle of theCayley projective plane, Jean Leray ’99 Conference Proceedings, pp. 163-182,
in Math. Phy. Studies 24(2003), Kluwer academic publishers.
(37) B. Booss-Bavnbeck, Kenro Furutani and Krzysztof P. Wojciechowski, The Geometry of Cauchy Data Spaces Jean Leray ’99 Conference Proceedings, pp.
321-354 (2003), in Math. Phy. Studies Vol. 24, Kluwer academic publishers.
(38) Kenro Furutani, Quantization of the Geodesic Flow on Quarternion Projective
Spaces, Annals of Global Analysis and Geometry, Vol. 22, No. 1, 1–27(2002).
(39) Bernhelm Booss-Bavnbek, Kenro Furutani and Nobukazu Otsuki, Criss-Cross
reduction of the Maslov index and a proof of Yoshida-Nicolaescu Spectral flow
formula, Tokyo Journal of Mathathematics. Vol. 24, No. 1, 113-128 (2001).
(40) Bernhelm Booss-Bavnbek and Kenro Furutani, Symplectic Functional Analysis
and Spectral Invariants, AMS Contemporary Mathematics, Vol. 242, 53-79(1999).
(41) Bernhelm Booss-Bavnbek and Kenro Furutani, The Maslov Index:a Functional
Analytical Definition and the Spectral Flow Formula, Tokyo Jounal of Mathematics, Vol. 21, No. 3, 1-34 (1998).

4(42) Kenro Furutani, The Heat Kernel and The Spectrum of A Class of Nilmanifolds, Communications in Partial Diﬀerential Equations, Vol. 21(3&4), 423-438(1996).
(43) Kenro Furutani and Shintarou Yoshizawa, A Kähler structure on the punctured
cotangent bundle of complex and quaternion projective spaces and its application to a geometric quantization II, Japanese Journal of Math., Vol. 21, No.
2, 355-392 (1995).
(44) Kenro Furutani and Ryuichi Tanaka, A Kähler structure on the punctured
cotangent bundle of complex and quaternion projective spaces and its application to a geometric quantization I, Journal of Math. of Kyoto Univ. Vol.34,
No. 4, 719–737 (1994).
(45) Kenro Furutani and Nobukazu Otsuki, Spectral flow and intersection number,
Journal of Math. of Kyoto Univ. Vol. 33, No. 1, 261–283 (1993).
(46) Kenro Furutani, Kei Sagami and Nobukazu Otsuki, The spectrum of the Laplacian on a certain nilpotent Lie groups, Communications in Partial DiﬀerentialEquations. Vol.18, No. 3, 533–555 (1993).
(47) Nobukazu Otsuki, Kenro Furutani, Spectral flow and Maslov index arising from
Lagrangian intersections, Tokyo J. Math. 14, No. 1, 135-150 (1991).
(48) Kenro Furutani, On a diﬀerentiable map commuting with an elliptic pseudodiﬀerential operator, J. Math. Kyoto Univ. 24, 197-203 (1984).
(49) Kenro Furutani, On an isomorphism of the algebra of pseudo-diﬀerential operators, J. Math. Kyoto Univ. 24, 269-274 (1984).
(50) Kenro Furutani, On the group of diﬀeomorphisms commuting with an ellipticoperator, J. Math. Soc. Japan 35, 153-162 (1983).
(51) Kenro Furutani, On eigenvalues and eigenspaces of a Laplace operator on thesphere S n , TRU Math. 17, No. 2, 273-283 (1981).
(52) Kenro Furutani, On a stability of essential spectra of Laplace operators on noncompact Riemannian manifolds, Proc. Jap. Acad., Ser. A 56, 425-428 (1980).
(53) Kenro Furutani, A group of isometries and eigenspaces of a Laplace operator
on S 2 , TRU Math. 15, No. 1, 19-22 (1979).
(54) Kenro Furutani, A note on the Arens-Royden theorem for real Banach algebras,
TRU Mathematics 11, 5-8 (1975).

(B) 単 行 本
• O.Calin, D-C. Chang, K. Furutani and C. Iwasaki, Heat Kernels for Ellipticand Sub-eliiptic Operators Method and Techniques, Applied and Numerical HarmonicAnalysis, 19(2010), 451 pages, Birkhäuser.
(C) 査 読 な し5(1) Wolfram Bauer, Kenro Furutani, Chisato Iwasaki, On the heat kernel on forms
on the Heisenberg group RIMS Kokyuroku (Symmetry and Singularity of Geometric Structures and Diﬀerential Equations)，No.2137, 17 pages (2019).
(2) Wolfram Bauer, Kenro Furutani, Spectral zeta functions of a Riemannian manifold of positive constant curvature, Proceeding of the “Sophia symposium2007” Modern mathematics and its applications to modern Technology, 1.-3.
Nov., pp. 82-88 (2007).
(3) Kenro Furutani, Complexified Hopf fibration and a pseudo-diﬀerential operator,RIMS Kokyuroku (Analytic Function Spaces and Their Operators)，No.1519,
pp. 38–58(2006).
(4) Kenro Furutani and Chisato Iwasaki Grushin operator and heat kernel on nilpotent Lie groups, RIMS Kokyuroku (Developments of Cartan Geometry andRelated Mathematical Problems)，No.1502, pp. 173–184(2006).
(5) Kenro Furutani and Serge de Gosson, Determinant of Laplacians on Heisenberg
Manifolds, Reports from MSI (School of Mathematics and System Engineering)at Växjö University, No. 03004 Jan 2003.
(D) 準 備 中
(1) Kenro Furutani, Chisato Iwasaki, Daisuke Tarama, Radon transformation andFourier integral operator.
(2) Kenro Furutani, Chisato Iwasaki, Fucks-type diﬀerential eqaution and symbolic
calculus on manifolds with conical singularities.
(3) Kenro Furutani, Irina Markina, Uniform discrete subgroups of pseudo H-type
Lie groups.