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Quantum probabilistic approach to the Segal-Bargmann transform and infinitely divisible laws

Research Project

Project/Area Number 23540131
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionAichi University of Education

Principal Investigator

ASAI Nobuhiro  愛知教育大学, 教育学部, 准教授 (60399029)

Co-Investigator(Renkei-kenkyūsha) KUBO Izumi  広島大学, 大学院・理学研究科, 名誉教授 (70022621)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords量子確率論 / 直交多項式 / シーガル・バーグマン変換 / ブレンケ型母関数 / q類似 / q直交多項式 / Boas-Buck型母関数 / q超幾何級数 / Brenke-Chihara問題 / q変形直交多項式 / ヤコビ・セゲーパラメータ / q変形超幾何級数
Research Abstract

From the point of multiplicative renormalization method, we examined the Brenke-Chihara problem, which is to determine all orthogonal polynomials associated with the Brenke type generating functions. As a result, all of the Jacobi-Szego parameters and q-hypergeometric series representations for all MRM-factors are obtained, explicitly. Our paper was published from IDAQP, an international mathematics journal. We have begun to consider if there would exist q-Fourier or q-Segal-Bargmann transforms and associated convolution products in a meaningful way from the quantum(algebraic) probabilistic view point.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (26 results)

All 2013 2012 2011

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (24 results) (of which Invited: 4 results)

  • [Journal Article] The Brenke type generating functions and explicit forms of MRM-triples by means of q-hypergeometric series2013

    • Author(s)
      N. Asai, I. Kubo, and H-H. Kuo
    • Journal Title

      Infinite Dimensional Analysis, Quantum Probability and Related Topics

      Volume: Vol.16 Issue: 02 Pages: 1350010-1350010

    • DOI

      10.1142/s0219025713500100

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Probability measures on C arising from the Jacobi-Szego parameters for continuous dual Hahn polynomials2011

    • Author(s)
      Nobuhiro Asai
    • Journal Title

      Infinite Dimensional Analysis, Quantum Probability and Related Topics

      Volume: 14 ( 3 ) Issue: 03 Pages: 361-374

    • DOI

      10.1142/s0219025711004493

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] On the Brenke-Chihara's orthogonal polynomials and related topics2013

    • Author(s)
      浅井暢宏
    • Organizer
      RIMS研究集会「量子場の数理とその周辺」
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Year and Date
      2013-10-03
    • Related Report
      2013 Final Research Report
  • [Presentation] The Boas-Buck generating functions and non-classical convolutions2013

    • Author(s)
      N. Asai
    • Organizer
      The 34th Conference on Quantum Probability and Related Topics
    • Place of Presentation
      Steklov Mathematical Institute(モスクワ, ロシア)
    • Year and Date
      2013-09-20
    • Related Report
      2013 Final Research Report
  • [Presentation] The Brenke-Chihara polynomials and q-convolutions2013

    • Author(s)
      N. Asai
    • Organizer
      The 8th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability
    • Place of Presentation
      National Institute for Mathematical Sciences (太田, 韓国)
    • Year and Date
      2013-08-22
    • Related Report
      2013 Final Research Report
  • [Presentation] On the classification of orthogonal polynomials having generating functions of the Boas-Buck type2013

    • Author(s)
      N. Asai
    • Organizer
      The Asian Mathematical Conference 2013, Probability /Stochastic Process/Statistics Session
    • Place of Presentation
      Bexco (釜山, 韓国)
    • Year and Date
      2013-07-03
    • Related Report
      2013 Final Research Report
  • [Presentation] MRM-triples and Boas-Buck generating functions2013

    • Author(s)
      I. Kubo
    • Organizer
      Workshop on IDAQP-White noise, Quantum information and statistics
    • Place of Presentation
      愛知県立大学(愛知県長久手町)
    • Year and Date
      2013-01-08
    • Related Report
      2013 Final Research Report
  • [Presentation] On the Brenke-Chihara's orthogonal polynomials and related topics2013

    • Author(s)
      Nobuhiro Asai
    • Organizer
      RIMS研究集会 量子場の数理とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] The Boas-Buck generating functions and non-classical convolutions2013

    • Author(s)
      Nobuhiro Asai
    • Organizer
      The 34th Conference on Quantum Probability and Related Topics
    • Place of Presentation
      Steklov Mathematical Institute of Russian Academy of Sciences (Moscow, Russia)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The Brenke-Chihara polynomials and q-convolutions2013

    • Author(s)
      Nobuhiro Asai
    • Organizer
      The 8th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability
    • Place of Presentation
      NIMS (Daejeon, Korea)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the classification of orthogonal polynomials having generating functions of the Boas-Buck type2013

    • Author(s)
      Nobuhiro Asai
    • Organizer
      The Asian Mathematical Conference 2013
    • Place of Presentation
      Bexco (Busan,Korea)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Orthogonal polynomials originated from the Boas-Buck type generating functions2012

    • Author(s)
      N. Asai
    • Organizer
      The 33th Conference on Quantum Probability and Related Topics
    • Place of Presentation
      Centre International de Rencontres Math'ematiques (マルセイユ, フランス)
    • Year and Date
      2012-10-01
    • Related Report
      2013 Final Research Report
  • [Presentation] マイクスナーおよびブレンケクラスに属する直交多項式系とその周辺2012

    • Author(s)
      浅井暢宏
    • Organizer
      RIMS研究集会「量子ウォークとその周辺」
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Year and Date
      2012-08-23
    • Related Report
      2013 Final Research Report
  • [Presentation] On the Brenke-Chihara problem and q-orthogonal polynomials2012

    • Author(s)
      N. Asai
    • Organizer
      The 7th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability
    • Place of Presentation
      Chungbuk National University (清州, 韓国)
    • Year and Date
      2012-07-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Brenke 型母関数とq直交多項式について2012

    • Author(s)
      浅井暢宏, 久保泉, 郭輝雄
    • Organizer
      日本数学2012年度年会統計数学分科
    • Place of Presentation
      東京理科大学, 神楽坂
    • Year and Date
      2012-03-26
    • Related Report
      2013 Final Research Report
  • [Presentation] MRM triples associated with Brenke type generating functions2012

    • Author(s)
      N. Asai
    • Organizer
      AMS-MAA Joint Mathematical Meeting
    • Place of Presentation
      Hynes Convention Center (ボストン, アメリカ)
    • Year and Date
      2012-01-04
    • Related Report
      2013 Final Research Report
  • [Presentation] Orthogonal polynomials originated from the Boas-Buck type generating functions2012

    • Author(s)
      Nobuhiro Asai
    • Organizer
      The 33th Conference on Quantum Probability and Related Topics
    • Place of Presentation
      CIRM, Luminy, France
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] マイクスナーおよびブレンケクラスに属する直交多項式系とその周辺2012

    • Author(s)
      浅井暢宏
    • Organizer
      京都大学数理解析研究所短期共同研究集会 量子ウォークとその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
  • [Presentation] On the Brenke-Chihara problem and q-orthogonal polynomials2012

    • Author(s)
      Nobuhiro Asai
    • Organizer
      The 7th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability
    • Place of Presentation
      忠北大学,清洲,韓国
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Brenke 型母関数と q 直交多項式について2012

    • Author(s)
      浅井暢宏
    • Organizer
      日本数学会2012年度年会統計数学分科会
    • Place of Presentation
      東京理科大学理学部
    • Related Report
      2011 Research-status Report
  • [Presentation] MRM Triples Associated with Brenke Type Generating Functions2012

    • Author(s)
      Nobuhiro Asai
    • Organizer
      AMS-MAA Joint Mathematis Meeting, Special Session on Stochastic Analysis.(招待講演)
    • Place of Presentation
      ハインズ・コンベンションセンター ( ボストン , 米国 )
    • Related Report
      2011 Research-status Report
  • [Presentation] ブレンケ型母関数と付随する直交多項式の分類について2011

    • Author(s)
      浅井暢宏
    • Organizer
      科研費研究集会「直交多項式と特殊関数が関わる確率論的諸問題とその周辺」
    • Place of Presentation
      名城大学名駅サテライト(名古屋市)
    • Year and Date
      2011-12-24
    • Related Report
      2013 Final Research Report
  • [Presentation] MRM-triple とStein's principle2011

    • Author(s)
      久保泉, 浅井暢宏
    • Organizer
      科研費研究集会「直交多項式と特殊関数が関わる確率論的諸問題とその周辺」
    • Place of Presentation
      名城大学名駅サテライト(名古屋市)
    • Year and Date
      2011-12-24
    • Related Report
      2013 Final Research Report
  • [Presentation] The Brenke type generating functions and orthogonal polynomials2011

    • Author(s)
      N. Asai
    • Organizer
      14th Workshop : Non-Commutative Harmonic Analysis
    • Place of Presentation
      The Mathematical Research and Conference Center (ベドレボ, ポーランド)
    • Year and Date
      2011-09-26
    • Related Report
      2013 Final Research Report
  • [Presentation] The Brenke Type Generating Functions and Orthogonal Polynomials.2011

    • Author(s)
      Nobuhiro Asai
    • Organizer
      14th Workshop: Non-Commutative Harmonic Analysis.  (招待講演)
    • Place of Presentation
      MRCC ( ベドレボ , ポーランド )
    • Related Report
      2011 Research-status Report
  • [Presentation] ブレンケ型母関数と付随する直交多項式の分類について2011

    • Author(s)
      浅井暢宏
    • Organizer
      直交多項式と特殊関数が関わる確率論的諸問題とその周辺
    • Place of Presentation
      名城大学名駅サテライト
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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