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Spectral and Scattering Theory and its Application

Research Project

Project/Area Number 09640151
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionOkayama University (1998)
Ibaraki University (1997)

Principal Investigator

TAMURA Hideo  Okayama University・Science Prof., 理学部, 教授 (30022734)

Co-Investigator(Kenkyū-buntansha) KAWASHITA Mishio  Ibaraki University・Edication Assistant Prof., 教育学部, 助教授 (80214633)
ONISHI Kazuei  Ibaraki University・Science Prof., 理学部, 教授 (20078554)
IWATSUKA Akira  Kyoto Institute of Technology Prof., 繊維学部, 教授 (40184890)
TANAKA Katumi  Okayama University・Science Assistant Prof., 理学部, 助教授 (60207082)
KATSUDA Atsushi  Okayama University・Science Assistant Prof., 理学部, 助教授 (60183779)
相羽 明  茨城大学, 理学部, 助手 (90202457)
松久 富美子  茨城大学, 理学部, 助教授 (90194208)
日合 文雄  茨城大学, 理学部, 教授 (30092571)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1997: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordsexponential product formula / Schrodinger semigroup / Pauli operator / asymptotic distribution of eigenvalues / scattering by magnetic fields / scattering amplitudes / レゾルベント / 固有値分布 / 非一様磁場
Research Abstract

The present project has been devoted to the study on the following three subjects related to the spectral and scattering theory for Schr_dinger operators.
(1) For exponential product formula(Lie-Trotter-Kato product formula), the convergence in operator norm has been proved and the error estimate has been also established. The 9btained results have been applied to Schr_dinger semi-groups or propagators with singular or time-dependent potentials.
(2) The unperturbed Pauli operator without electric potentials has zero eigenvalue with infinite multiplicities as its bottom of essential spectrum. When the operators are perturbed by potentials falling off at infinity, the asymptotic distribution of discrete eigenvalues near the origin has been studied. The special emphasis is placed on the case that Pauli operators do not necessarily have constant magnetic fields.
(3) The asymptotic behavior at low energy of scattering amplitudes has been analysed for scattering by two dimensional magnetic fields and the relation to scattering by magnetic fields with small support has been also discussed.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] H.Tamura: "Error bounds on exponential product formulas for Sahiodinger operators" J.Math.Soc.Japan. 50. 359-377 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura: "Error bound in trace norm for Trotter-Kato product formula of Gibby sencigroups" Asymptotic Analysis. 17. 239-266 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura: "Error estimate in operator norm of exponential product formula for propagators of parabolic equations" Osaka Math. J.35. 751-770 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with spherically symmetric magnetic fields" Tsukuba J. Math.22. 281-303 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura: "Asymptotic distribution of eigenvalues for Pauli operators with nonconstant magnetic fields" Duke Math. J.93. 535-574 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields" Ann.Inst.Fourier (Grenoble). 48. 479-515 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura, A.Doumeki and T.Ichinose: "Error bounds on exponential product formulas for Schrodinger operators" J.Math.Soc.Japan. 50. 359-377 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura and T.Ichinose: "Error bound in trace norm for Trotter-Kato product formula of Gibbs semigroups" Asymptotic Analysis. 17. 239-266 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura and T.Ichinose: "Error estimate in operator norm exponential product formula for propagators of parabolic equations" Osaka Math.J.35. 751-770 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura and A.Iwatsuka: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with spherically symmetric magnetic fields" Tsukuba J.Math.22. 281-303 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura and A.Iwatsuka: "Asymptotic distribution of eigenvalues for Pauli operators with nonconstant magnetic fields" Duke Math.J. 93. 535-574 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura and A.Iwatsuka: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields" Ann.Inst.Fourier (Grenoble). 48. 479-515 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Tamura: "Euor bounds on exponeutial product farmulas for Sohiodinger operators" J.Math.Soc.Japan. 50. 359-377 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Tamura: "Euor bound in trace norm for Trotter-Kato product formula of Gibbs semigrsecps" Asepuptotic Analysis. 17. 239-266 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Tamura: "Euor estimate in operator norm of exponential product formula for propagators of parabolic equations" Osaka Math.J.35. 751-770 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Tamura: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with spherically symnetric magnetic fields" Tsukuba J.Math.22. 281-303 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Tamura: "Asymptotic distribution of eigenvalues for Pauli operators with noncarstant magnetic fields" Duke Math.J.93. 535-574 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Tamura: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with noncoustant magnetic fields" Ann.Inst.Fourier(Grenoble). 48. 479-515 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 田村英男: "Error estimate in operator norm for Trotter-Kato product formula" Inteyrcl Equation and Operator Theory. 27. 195-207 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 田村英男: "Semi-classical bound on scattering cross sections in two dimensional magnetic fields" Nagoya math.J.148(発表予定). (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 田村英男: "Error bounds on oxponentical product formulas for Schrodiger Operators" J.Math Soc.Japan. 50(発表予定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 田村英男: "Asymptotic distribution of evgenvalner for Pauli operators with nonconstant magnetic fields" Duke Math.J. (発表予定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 田村英男: "Asymptotic distribution of Negative eigenvelueu for two dimensional Pauli operators with nonconstant magnetic fields" Am.Inst.Fowier内. (発表予定). (1998)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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