Researcher Directory | Aichi University of Education.


detailes

Asai Nobuhiro

  • Faculty:Department of MathematicsPosition:Professor
  • Address:1 Hirosawa,Igaya-cho,Kariya-shi,Aichi
  • TEL:FAX:
  • E-mail address:
  • Web site:
Modified:05/08/2019

Profile

Assigned Class

  • Natural Sciences

Research Field

  • Functional Analysis, Probability theory, White noise theory
  • Keywords:Infinite dimensional analysis , Quantum probability theory , Mathematical physics , Theory of orthogonal polynomials , Fock spaces , q-deformation

Current Subject

  • Non-commutative processes on defomed Fock spaces

  • Non-Gaussian Segal-Bargmann analysis in quantum probability theory

  • White noise theory and its applications to quantum probability theory

  • The construction of orthogonal polynomials by the multiplicative renormalization method

Academic Societies

Academic Societies
  • The Mathematical Society of Japan
  • The American Mathematical Society
  • The Japan Society for Industrial and Applied Mathematics

Academic Background

Degree
  • Ph.D

Research Career

Research Career
  • 2008 - , Associate Professor
  • 2006 - 2008 , Assistant Professor

Research

Books, Articles, etc.

Articles
  • (with H. Yoshida)
    Poisson type operators on the Fock space of type B
    Journal of Mathematical Physics, American Institute of Physics, 60(1):011702, 2019
    MR3903542
  • On weighted Fock spaces and distributions (Mathematical Aspects of Quantum Fields and Related Topics)
    RIMS Kokyuroku, RIMS, Kyoto University, 2089:84--94, 2018-08
  • (with M. Bozejko and T. Hasebe)
    Radial density function associated with the $(\alpha,q)$-Fock space
    Mathematical quantum field theory and related topics, MI Lecture note series, Institute for Mathematics for Industry, Kyusyu University, 72:90--98, 2017-01
  • (with A. Krystek and L. Wojakowski)
    Interpolations of Bargmann type measures
    Demonstratio Mathematica, De Gruyter, 49(3):293–301, 2016
    MR3540972
  • (with M. Bozejko and T. Hasebe)
    Radial Bargmann representation for the Fock space of type B
    Journal of Mathematical Physics, American Institute of Physics, 57(2):021702 (13 pages), 2016
    MR3447642
  • Notes on some orthogonal polynomials having the Brenke type generating functions (Mathematical aspects of quantum fields and related topics)
    RIMS Kokyuroku, RIMS, Kyoto University, 1921:41-53, 2014-10
  • (with I. Kubo and H.-H. Kuo)
    The Brenke type generating functions and explicit forms of MRM-triples by means of q-hypergeometric series
    Infinite Dimensional Analysis, Quantum Probability and Related Topics., World Scientific, 16(2):1350010, 2013
    MR3078821
  • Probability measures on C arising from the Jacobi-Szego parameters for continuous dual Hahn polynomials
    Infinite Dimensional Analysis, Quantum Probability and Related Topics., World Scientific, 14(3):361-374, 2011
    MR2847244
  • The construction of subordinated probability measures on C associated with the Jacobi-Szegö parameters.
    Infinite Dimensional Analysis, Quantum Probability and Related Topics., World Scientific, 12:401-411, 2009
    MR 2011b:46102
  • Hilbert space of analytic functions associated with a rotation invariant measure.
    Quantum Probability and Related Topics., World Scientific, :49-62, 2008
    MR 2011a:46110
  • Riesz potentials derived by one-mode interacting Fock space approach.
    Colloquium Mathematicum., 109:101-106, 2007
    MR 2008f:46090.
  • (with I. Kubo and H.-H. Kuo)
    Renormalization, orthogonalization, and generating functions
    Quantum Information V., World Scientific, , :49-56, 2006
  • On Gaussian and Poisson white noises
    Quantum Information V., World Scientific, , :35-48, 2006
  • Hilbert space of analytic functions associated with the modified Bessel function and related orthogonal polynomials.
    Infinite Dimensional Analysis, Quantum Probability and Related Topics. , World Scientific, 8:505-514, 2005
    MR 2006g:30085.
  • (with I.Kubo and H.-H. Kuo)
    Generating function method for orthogonal polynomials and Jacobi-Szegö parameters
    M. Schürmann et al. (eds.) Quantum Probability and Infinite Dimensional Analysis-From Foundation to Applications., World Scientific, , :42-55, 2005
    MR 2007b:33010.
  • (with I. Kubo and H.-H. Kuo)
    Multiplicative renormalization and generating functions II
    Taiwanese Journal of Mathematics., 8(4):593-628, 2004
    MR 2005i:33008.
  • (with I. Kubo and H.-H. Kuo)
    Generating functions of orthogonal polynomials and Szegö-Jacobi parameters
    Probability and Mathematical Statistics., 23(2):273-291, 2003
    MR 2005g:42057.
  • (with I. Kubo and H.-H. Kuo)
    Gaussian and Poisson white noises with related characterization theorems.
    Contemporary Mathematics., Amer. Math. Soc., 317:45-56, 2003
    MR 2004d:60179.
  • (with I. Kubo and H.-H. Kuo)
    Multiplicative renormalization and generating functions I.
    Taiwanese Journal of Mathematics., 7(1):89-101, 2003
    MR 2004a:33010.
  • (with I. Kubo and H.-H. Kuo)
    Segal-Bargmann transforms of one-mode interacting Fock spaces associated with Gaussian and Poisson measures.
    Proc. Amer. Math. Soc., 131(3):815-823, 2003
    MR 2003j:46099.
  • Integral transform and Segal-Bargmann representation associated to q-charlier polynomials.
    Quantum Information IV., World Scientific, , :39-48, 2002
    MR 2004a:81137.
  • On quantum white noises and related transformations
    RIMS Kokyuroku., RIMS, Kyoto University,, (1278):34-47, 2002
  • Analytic characterization of one-mode interacting Fock space.
    Infinite Dimensional Analysis, Quantum Probability and Related Topics., 4:409-415, 2001
    MR 2002k:81107.
  • (with I. Kubo and H.-H. Kuo)
    General characterization theorems and intrinsic topologies in white noise analysis.
    Hiroshima Math. J., 31:299-330, 2001
    MR 2002f:60131.
  • Chracterization of product measures by an integrability condition.
    Quantum Information III., World Scientific, , :21-33, 2001
    MR 2002m:60123.
  • (with I. Kubo and H.-H. Kuo)
    Roles of log-concavity, log-convexity, and growth order in white noise analysis.
    Infinite Dimensional Analysis, Quantum Probability and Related Topics., 4:59-84, 2001
    MR 2002a:46055.
  • (with I. Kubo and H.-H. Kuo)
    Bell numbers, log-concavity, and log-convexity
    Acta Appl. Math., 63:79-87, 2000
    MR 2002f:60130.
  • (with I. Kubo and H.-H. Kuo)
    Characterization of test functions in CKS-space
    S. Albeverio et al. (eds.) Mathematical Physics and Stochastic Analysis, , World Scientific, , :68-78, 2000
    MR 2002m:46068.
  • (with I. Kubo and H.-H. Kuo)
    CKS-space in terms of growth functions
    Quantum Information II., World Scientific, , :17-27, 2000
    MR 2002k:60139.
  • (with I. Kubo and H.-H. Kuo)
    Feynman integrals associated with Albeverio-H-egh-Krohn and Laplace transform potentials
    H. Kunita et al. (eds.) Stochastics in Finite and Infinite Dimensions, , Birkhäuser, , :29-48, 2000
    MR 2001k:60091.
  • (with I. Kubo and H.-H. Kuo)
    Characterization of Hida measures in white noise analysis
    H. Heyer et al. (eds.) Infinite Dimensional Harmonic Analysis- Transactions of a Japanese-Germany Symposium, , D.+M. Gräbner, Tübingen,, :70-83, 2000
    MR 2002f:46075.
  • A note on general setting of white noise triple and positive generalized functions
    RIMS Kokyuroku., RIMS, Kyoto University,, (1139):19--29, 2000
Presentations
  • 国際会議(以下作成中)
Others
  • 追加予定

Research Activities

Other Research Activities
  • 2019- , AMS-MAA Joint Mathematical Meeting, AMS Special session on Orthogonal Polynomials, Quantum Probability, Harmonic Analysis, and Stochastic Analysis , Baltimore Convention Center (Baltimore, USA)
  • Mathematical Review (AMS)
  • zbMATH

Education

Thesis Guidance

  • 2017, Graduation thesis Total:4, Master's thesis Total:1(1)
  • 2016, Graduation thesis Total:1, Master's thesis Total:2(1)
  • 2014, Graduation thesis Total:1, Master's thesis Total:1
  • 2013, Graduation thesis Total:2
  • 2012, Graduation thesis Total:7
  • 2011, Graduation thesis Total:5
  • 2010, Graduation thesis Total:6
  • 2009, Graduation thesis Total:7
  • 2008, Graduation thesis Total:7

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