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1992 Fiscal Year Final Research Report Summary

Potential-kernels of logarithmic type and their applications

Research Project

Project/Area Number 03452009
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionNagoya University

Principal Investigator

ITO Masayuki  Nagoya University College of General Education Professor, 教養部, 教授 (60022638)

Co-Investigator(Kenkyū-buntansha) NAGAI Hideo  General Education Associated Professor, 教養部, 助教授 (70110848)
IHARA Shunsuke  General Education Associated, 教養部, 教授 (00023200)
SATO Ken-iti  General Education Professor, 教養部, 教授 (60015500)
SUZUKI Noriaki  General Education Assistant Professor, 教養部, 講師 (50154563)
MURAI Takafumi  Nagoya University School of Sciences, College of Associated Professor, 理学部, 助教授 (00109266)
Project Period (FY) 1991 – 1992
KeywordsHunt convolution kernels / kernels of logarithmic type / Spectral synthetic / Analytic capacity / non-integrability of sub-harmonic functions / resolvent of potential-kernels / recurrent semi-group / Ornstein-Uhlenbeck type process
Research Abstract

By using some properties of potential-kernels of logarithmic type, we gave a definitive solution of the following well-known problem. "Does the totality of convolution kernels satisfying the domination principle coincide with the closure of the set of Hunt convolution kernels?" In this connection, we proved that a potential-kernel is spectral synthetic if it satisfies the domination principle. Applying to the theory of potential-kernels, we obtain that with a given potential-kernel satisfying the domination principle, its resolvent formed by nice potential-kernels is associated. Suggested by the sweeping-out process, we worked out an arc-variation to investigate the analytic capacity. In the study of the classical harmonic function theory, it is remarkable to determine domains on which non-zero subharmonic functions are not integrable.
Potential-kernels of logarithmic type possess recurrent semi-group,s which is closely related with the probability theory. In the study of the probability theory, we obtain a criterion of the transiency of Ornstein-Uhlenbeck type processes and results concerning optimal diffusion processes.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] M.Ito: "On the specxtral synthesis of potentials with respect to continuous function-kernels" Preprint series,Dept.of Math.College of Gen.Dduc.,Nagoya Univ.15. 1-22 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Murai: "Analytic capacity ofr arcs" Proc.Int.Nat.Conf.Math.Kyoto 1991. 1. 901-911 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Murai: "The arc-length variation of analytic capacity and a conformeal geometry" Nagoya Math.J.125. 151-216 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Suzuki: "Nonintegrability of superharmonic functions." Proc.Amer.Math.Soc.113. 113-115 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Sato and M.Yamazato: "Remarks on recurrence criteria for processes of Ornstein-Uhlenbeck type" To appera in Proc.Conf.Functional Analysis and related Topics 1991. (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Nagai: "Ergodic control problems on the whole Euclidean space and convergence of symmetric diffusions." Forum Math.4. 159-173 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Ito: "On the spectral synthesis of potentials with respect ot continuous function-kernels" Preprint series, Dept. of Math. College of Gen. Educ., Nagoya Univ.15. 1-22 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Murai: "Analytic capacity for arcs" Proc.Int.Nat.Conf.Mat.Kyoto 1991. 1. 901-911 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Murai: "The arc-length variation of analytic capacity and a conformal geometry" Nagoya Math. J.125. 151-216 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.Suzuki: "Nonintegrability of superharmonic functions" Proc. Amer. Math. Soc.113. 113-115 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Sato and M.Yamazato: "Remarks on recurrence criteria for processes of Ornstein-Uhlenbeck type" Proc. Conf. Functional Analysis and related Topics. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Nagai: "Ergodic control problems on the whole Euclidean space and convergence of symmetric diffusions" Forum Math.4. 159-173 (1992)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1994-03-24  

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