Research Papers Published in Journals

2011-latest

• 68] Un Cig Ji and Nobuaki Obata:
  Calculating normal-ordered forms in Fock space by quantum white noise derivatives.
  Interdiscip. Inform. Sci., 19(2):201-211, 2013.
  [DOI] 10.4036/iis.2013.201
• 67] Yuji Hibino, Hun Hee Lee, and Nobuaki Obata:
  Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs.
  Colloq. Math., 132:35-51, 2013.
  [DOI] 10.4064/cm132-1-4
• 66] Hun Hee Lee and Nobuaki Obata:
  Distance-k graphs of hypercube and q-Hermite polynomials,
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 16(2):1350011, 12pages, 2013.
  [DOI] 10.1142/S0219025713500112
• 65] Norio Konno, Nobuaki Obata, and Etsuo Segawa:
  Localization of the Grover walks on spidernets and free Meixner laws.
  Comm. Math. Phys., 322(3):667-695, 2013.
  [DOI] 10.1007/s00220-013-1742-x
• 64] Nobuaki Obata:
  Spectra of Manhattan products of directed paths P_n#P_2,
  Interdiscip. Inform. Sci., 18(1):43-54, 2012.
  [DOI] 10.4036/iis.2012.43
• 63] Nobuaki Obata.
  One-mode interacting Fock spaces and random walks on graphs.
  Stochastics, 84(2-3):383-392, 2012.
  [DOI] 10.1080/17442508.2010.550919
• 62] Nobuaki Obata.
  Manhattan products of digraphs: characteristic polynomials and examples.
  Ann. Funct. Anal., 3(2):135-143, 2012.
• 61] Nobuaki Obata.
  Asymptotic spectral distributions of distance k-graphs of large-dimensional hypercubes.
  Banach Center Publ., 96:287-292, 2012.
  [DOI] 10.4064/bc96-0-20
• 60] Nobuaki Obata and Habib Ouerdiane.
  A note on convolution operators in white noise calculus.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 14(4):661-674, 2011.
  [DOI] 10.1142/S0219025711004535
• 59] Nobuaki Obata.
  Markov product of positive definite kernels and applications to Q-matrices of graph products.
  Colloq. Math., 122(2):177-184, 2011.
  [DOI] 10.4064/cm122-2-2

2006-2010

• 58] Un Cig Ji and Nobuaki Obata.
  Implementation problem for the canonical commutation relation in terms of quantum white noise derivatives.
  J. Math. Phys., 51(12):123507, 15pages, 2010.
  [DOI] 10.1063/1.3516477
• 57] Yusuke Ide, Norio Konno, and Nobuaki Obata.
  Spectral properties of the threshold network model.
  Internet Math., 6(2):173-187, 2010.
• 56] Un Cig Ji and Nobuaki Obata.
  Quantum stochastic integral representations of Fock space operators.
  Stochastics, 81(3-4):367-384, 2009.
  [DOI] 10.1080/17442500902919645
• 55] Un Cig Ji and Nobuaki Obata.
  Quantum stochastic gradients.
  Interdiscip. Inform. Sci., 15(3):345-359, 2009.
  [DOI] 10.4036/iis.2009.345
• 54] Un Cig Ji and Nobuaki Obata.
  Annihilation-derivative, creation-derivative and representation of quantum martingales.
  Comm. Math. Phys., 286(2):751-775, 2009.
  [DOI] 10.1007/s00220-008-0702-3
• 53] Nobuaki Obata.
  Notions of independence in quantum probability and spectral analysis of graphs.
  Amer. Math. Soc. Transl. Ser. 2, 223:115-136, 2008.
• 52] Un Cig Ji and Nobuaki Obata:
  Generalized white noise operator fields and quantum white noise derivatives
  Semin. Congr., 16: 17-33, 2008
• 51] Akihito Hora and Nobuaki Obata.
  Asymptotic spectral analysis of growing regular graphs.
  Trans. Amer. Math. Soc., 360(2):899-923, 2008.
• 50] Nobuaki Obata.
  Positive Q-matrices of graphs.
  Studia Math., 179(1):81-97, 2007.
• 49] Song Liang, Nobuaki Obata, and Shuji Takahashi.
  Asymptotic spectral analysis of generalized Erdos-Renyi random graphs.
  Banach Center Publ., 78:211-229, 2007.
• 48] Un Cig Ji, Nobuaki Obata, and Habib Ouerdiane.
  Quantum Levy Laplacian and associated heat equation.
  J. Funct. Anal., 249(1):31-54, 2007.
• 47] Daisuke Igarashi and Nobuaki Obata.
  Asymptotic spectral analysis of growing graphs: Odd graphs and spidernets.
  Banach Center Publications, 73:245-265, 2006.
• 46] Nobuaki Obata.
  A note on Konno's paper on quantum walk.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 9(2):299-304, 2006.
• 45] Un Cig Ji and Nobuaki Obata.
  Unitarity of generalized Fourier-Gauss transforms.
  Stoch. Anal. Appl., 24(4):733-751, 2006.

2001-2005

• 44] Un Cig Ji and Nobuaki Obata.
  Unitarity of Kuo's Fourier-Mehler transform.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 7(1):147-154, 2004.
• 43] Un Cig Ji and Nobuaki Obata.
  A role of {B}argmann-{S}egal spaces in characterization and expansion of operators on {F}ock space.
  J. Math. Soc. Japan, 56(2):311-338, 2004.
  [DOI] 10.2969/jmsj/1191418632
• 42] Luigi Accardi, Anis Ben Ghorbal, and Nobuaki Obata.
  Monotone independence, comb graphs and Bose-Einstein condensation.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 7(3):419-435, 2004.
• 41] Nobuaki Obata.
  Quantum probabilistic approach to spectral analysis of star graphs.
  Interdiscip. Inform. Sci., 10(1) (2004), 41-52.
• 40] Un Cig Ji and Nobuaki Obata.
  A unified characterization theorem in white noise theory.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6(2):167-178, 2003.
• 39] Yukihiro Hashimoto, Akihito Hora, and Nobuaki Obata.
  Central limit theorems for large graphs: method of quantum decomposition.
  J. Math. Phys., 44(1):71-88, 2003.
• 38] Hui-Hsiung Kuo, Nobuaki Obata, and Kimiaki Saito.
  Diagonalization of the Levy Laplacian and related stable processes.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5(3):317-331, 2002.
• 37] Un Cig Ji, Nobuaki Obata, and Habib Ouerdiane.
  Analytic characterization of generalized Fock space operators as two-variable entire functions with growth condition.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5(3):395-407, 2002.
• 36] Dong Myung Chung, Un Cig Ji, and Nobuaki Obata.
  Quantum stochastic analysis via white noise operators in weighted Fock space.
  Rev. Math. Phys., 14(3):241-272, 2002.
• 35] Nobuaki Obata.
  Quadratic quantum white noises and Levy Laplacian.
  Nonlinear Analysis, Theory, Methods and Applications, 47:2437-2448, 2001.
• 34] Nobuaki Obata.
  Unitarity criterion in white noise calculus and nonexistence of unitary evolutions driven by higher powers of quantum white noises.
  Aportaciones Mat. Investig., 16:251-269, 2001.
• 33] Nobuaki Obata.
  Coherent state representation and unitarity condition in white noise calculus.
  J. Korean Math. Soc., 38(2):297-309, 2001.

1996-2000

• 32] Nobuaki Obata.
  Coherent state representations in white noise calculus.
  Can. Math. Soc. Conference Proceedings, 29:517-531, 2000.
• 31] Tetsuhiko Yoshida, Nobuaki Obata, and Oosawa Kenji.
  Color-coding reveals tandem repeats in the {E}scherichia coli genome.
  J. Mol. Biology, 298(3):343-349, 2000.
• 30] Nobuaki Obata.
  Complex white noise and coherent state representations.
  Acta Appl. Math., 63(1-3):283-291, 2000.
• 29] Nobuaki Obata.
  Wick product of white noise operators and quantum stochastic differential equations.
  J. Math. Soc. Japan, 51(3):613-641, 1999.
  [DOI] 10.2969/jmsj/05130613
• 28] Dong Myung Chung, Un Cig Ji, and Nobuaki Obata.
  Transformations on white noise functions associated with second order differential operators of diagonal type.
  Nagoya Math. J., 149:173-192, 1998.
• 27] Dong Myung Chung, Un Cig Ji, and Nobuaki Obata.
  Higher powers of quantum white noises in terms of integral kernel operators.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 1(4):533-559, 1998.
• 26] Luigi Accardi, Yukihiro Hashimoto, and Nobuaki Obata.
  Singleton independence.
  Banach Center Publ., 43:9-24, 1998.
• 25] Luigi Accardi, Yukihiro Hashimoto, and Nobuaki Obata.
  A role of singletons in quantum central limit theorems.
  J. Korean Math. Soc., 35(3):675-690, 1998.
• 24] Luigi Accardi, Yukihiro Hashimoto, and Nobuaki Obata.
  Notions of independence related to the free group.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top., 1(2):201-220, 1998.
• 23] Nobuaki Obata.
  Quantum stochastic differential equations in terms of quantum white noise.
  Nonlinear Analysis, Theory, Methods and Applications, 30:279-290, 1997.
• 22] Nobuaki Obata.
  Integral kernel operators on {F}ock space: generalizations and applications to quantum dynamics.
  Acta Appl. Math., 47(1):49-77, 1997.
• 21] Nobuaki Obata.
  Constructing one-parameter transformations on white noise functions in terms of equicontinuous generators.
  Monatsh. Math., 124(4):317-335, 1997.
• 20] Nobuaki Obata and Norman J. Wildberger.
  Generalized hypergroups and orthogonal polynomials.
  Nagoya Math. J., 142:67-93, 1996.

1991-1995

• 19] Nobuaki Obata.
  Generalized quantum stochastic processes on Fock space.
  Publ. Res. Inst. Math. Sci., 31(4):667-702, 1995.
• 18] Nobuaki Obata.
  Derivations on white noise functionals.
  Nagoya Math. J., 139:21-36, 1995.
• 17] Nobuaki Obata.
  Operator calculus on vector-valued white noise functionals.
  J. Funct. Anal., 121(1):185-232, 1994.
• 16] Nobuaki Obata.
  White noise delta functions and continuous version theorem.
  Nagoya Math. J., 129:1-22, 1993.
• 15] Nobuaki Obata.
  An analytic characterization of symbols of operators on white noise functionals.
  J. Math. Soc. Japan, 45(3):421-445, 1993.
  [DOI] 10.2969/jmsj/04530421
• 14] Takeyuki Hida, Hui-Hsiung Kuo, and Nobuaki Obata.
  Transformations for white noise functionals.
  J. Funct. Anal., 111(2):259-277, 1993.
• 13] Nobuaki Obata.
  Rotation-invariant operators on white noise functionals.
  Math. Z., 210(1):69-89, 1992.
• 12] Takeyuki Hida, Nobuaki Obata, and Kimiaki Saito.
  Infinite-dimensional rotations and Laplacians in terms of white noise calculus.
  Nagoya Math. J., 128:65-93, 1992.
• 11] Martin Bluemlinger and Nobuaki Obata.
  Permutations preserving Cesaro mean, densities of natural numbers and uniform distribution of sequences.
  Ann. Inst. Fourier (Grenoble), 41(3):665-678, 1991.

1987-1990

• 10] Nobuaki Obata.
  Integral expression of some indecomposable characters of the infinite symmetric group in terms of irreducible representations.
  Math. Ann., 287(3):369-375, 1990.
• 9] Nobuaki Obata.
  Construction of irreducible unitary representations of amalgams of discrete abelian groups.
  J. Math. Soc. Japan, 42(4):585-603, 1990.
  [DOI] 10.2969/jmsj/04240585
• 8] Nobuaki Obata.
  A characterization of the Levy Laplacian in terms of infinite-dimensional rotation groups.
  Nagoya Math. J., 118:111-132, 1990.
• 7] Hui-Hsiung Kuo, Nobuaki Obata, and Kimiaki Saito.
  Levy Laplacian of generalized functions on a nuclear space.
  J. Funct. Anal., 94(1):74-92, 1990.
• 6] Nobuaki Obata.
  Some remarks on induced representations of infinite discrete groups.
  Math. Ann., 284(1):91-102, 1989.
• 5] Nobuaki Obata.
  A note on certain permutation groups in the infinite-dimensional rotation group.
  Nagoya Math. J., 109:91-107, 1988.
• 4] Nobuaki Obata.
  Density of natural numbers and the Levy group.
  J. Number Theory, 30(3):288-297, 1988.
• 3] Nobuaki Obata.
  Analysis of the Levy Laplacian.
  Soochow J. Math., 14(1):105-109, 1988.
• 2] Nobuaki Obata.
  Certain unitary representations of the infinite symmetric group II.
  Nagoya Math. J., 106:143-162, 1987.
• 1] Nobuaki Obata.
  Certain unitary representations of the infinite symmetric group I.
  Nagoya Math. J., 105:109-119, 1987.