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.

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