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2000 Fiscal Year Final Research Report Summary

Applications of analyticoty of functions

Research Project

Project/Area Number 10304009
Research Category

Grant-in-Aid for Scientific Research (A).

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionGunma University

Principal Investigator

SAITOH Saburou  Faculty of Engineering, Gunma University, Professor, 工学部, 教授 (10110397)

Co-Investigator(Kenkyū-buntansha) MORI Seiki  Yamagata University. Science Dept. Professor, 理学部, 教授 (80004456)
HAYASHI Nakao  Tokyo Science University Science Dept. Professor, 理学部, 教授 (30173016)
SAKAI Makoto  Tokyo Metropolitan University Science Dept. Professor, 理学研究科, 教授 (70016129)
YAMAMOTO Masahiro  University of Tokyo, Math.Sci. Associated Professor, 大学院・数理科学研究科, 助教授 (50182647)
SIGA Hirosige  Tokyo Institute of Technology. Science Dept. Professor, 理学部, 教授 (10154189)
Project Period (FY) 1998 – 2000
KeywordsAnalytic function / reproducing kernel / inverse problem / differential equ / numerical / Riemann surface / Integral transform / Klein group
Research Abstract

(1) About mathematics, we discussed and gave the definitions of mathematics and good results in mathematics. In particular, the essentials of mathematics are stated to be relations. As an example in this sprit, we established a method connecting "analyticity of functions" and "nonlinear transforms" and derived various concrete results.
(2) We found a method discussing the existence of the solutions for general linear differential equations with variable coefficients. This method gives also a contructing algorithms of the solutions, when there exist the solutions.
(3) For many solutions for linear partial differential equations depending time, we found a general principle representing the solutions by means of their local deta in both space and time. We can get similar results for many elliptic linear partial differential equations. This pleasant result was named as "Principle of Telethoscope"
(4) We found a general principle introducing various operators among Hilbert spaces by mens of transforms. In particular, we were able to give a general definition of the fundamental operators "convolution". As a very simple case, we derived a very simple and beautiful convolution inequality which is different from the famous Young inequality in the convolution.
(5) In the viewpoint of conformal mappings, we found very nice representation formulas and their error estimates in the representations of analytic functions in terms of their local deta, using the Riemannn mapping function.
(6) We continued the research for real inversion formulas of the Laplace transform from three directions ; that is, uniformly convergence formulas, error estimates and conditional stability.

  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] S.Saitoh: "Various operators in Hulbert space introduced by transforms"International J. of Applied Mathematics. 1. 111-126 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Amano,S.Saitoh and M.Yamamoto: "Error estimates of the real inversion formulas of the Laplace transform"Integral Transforms and Special Functions. 10. 1-14 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Amano,S.Saitoh and A.Syarif: "A real inversion formula for the Laplace transform in a Sobolev space"Zeits chrift fur Analysis and ihre Anwendungen. 18. 1031-1038 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] V.K.Tuan,S.Saitoh,M Yamamoto: "Reverse weighted C_p-norm in equalities in convolution and Stability in inverse problems"J.of Inequclities in Pure and Applied Math.. 1. No.7 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Saitoh: "Representations of the solutions of partial differential equations of parabolic and hyperbolic types by means of * observations"Applicable Analysis. (in press).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Saitoh,M.Mori: "Representations of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. (in press).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Saitoh 他(編集): "Reproducing Kernels and their Applications"Kluwer Acadmic Publishers. 234 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Saitoh 他(編集): "Analytic Extension Formulas and their Applications"Kluwer Acadmic Publishers. 285 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Linear integro-differential equations and their applications: "Volterra Equations and Applications"(ed. by C.Corduneanu and I.W.Sandbery) Gordon and Breach Sci. Publishers. 433-440 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Saitoh and M.Yamamoto: "Integral transforms involving smooth functions"Reproducing kernels and their applications Kluwer Academic Publishers Boston. 149-163 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] "Applications of the general theory of reproducing kernels"Reproducing kernels and their applications kluwer Academic Publishers Boston. 165-188 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] "Nonlinear transforms and analyticity of functions"Nonlinear Mathematical Analysis and its Applications Hadronic Press.Inc.Florida, USA. 223-234 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] "Various operators in Hilbert space introduced by transforms"International J.of Applied Mathematics. 1. 111-126 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] G.Nakamura, S.Saitoh and A.Syarif: "Representations and harmonic extension formulas of harmonic functions on half spaces"Complex Variables. 42. 323-332 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] G.Nakamura, S.Saitoh and A.Syarif: "Representations of initial heat distributions by means of their heat distribu as functions of time"Inverse Problems. 15. 1255-1261 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] "Survey on Classical Inequalities, Weighted L_p-norm inequalities in convolutions"Kluwer Acadmic Publischers. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Amano, S.Saitoh and M.Yamamoto: "Error estimates of the real inversion formulas of the Laplace transform"Integral Transforms and Special Functions. 10. 1-14 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Amano, S.Saitoh and A.Syarif: "A Real Inversion Formulas for the Laplace Transform in a Sobolev Space"Zeitschrift fur Analysis und ihre Anwendungen. 18. 1031-1038 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Saitoh, V.K.Tuan and M.Yamamoto: "Reverse weighted L_p-norm inequalities in convolutions and stability in inverse problems J.of Inequalities"Pure and Applied Mathematics. 1 No.7. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] V.K.Tuan, S.Saitoh and M.Saigo: "Size of support of initial heat distribution in the ID heat equation Applicable Analysis"74. 439-446 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Inverse source problems in the Helmholtz equation: "Inverse=problems and related topics"Chapman & Hall/CRC Research Notes in Mathematics. 419. 133-143 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] "Representations of the solutions of partial differential equations of parabolic and hyperbolic types by means of time obserations Applicable Analysis"(in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Saitoh, D.Alpay, J.A.Ball and T.Ohsawa (edited): "Kiuwer Academic Publishers. Boston/Dordrecht/London, International Society for Analysis, Applications and Computation""Reproducing kernels and their applications" Vol.3. 234 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] G.Nakamura, S.Saitoh, J.K.Seo and M.Yamamoto (edited): "Chapman & Hall/CRC Research Notes in Mathematics 419 Chapman & Hall/CRC UK""Inverse problems and related topics, ". 232 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] D.E.Edmunds, P.K.Jain, P.Jain, A.Kufner, L.E.Persson and S.Saitoh (edited): "Narosa Publishing House, India""Function Spaces and Applications". 278 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S.Saitoh, N.Hayashi and M.Yamamoto (edited): "Kluwer Academic Publishers. Boston/Dordrecht/London, International Society for Analysis, Applications and Computation""Analytic Extension Formulas and their Applications". 285 (2001)

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

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Published: 2002-03-26  

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