List of Publications of Hitoshi Kitada

  1. A stationary approach to long-range scattering, Osaka J. Math., 13 (1976), 311-333.
  2. On the completeness of modified wave operators, Proc. Japan Acad., 52 (1976), 409-412.
  3. Scattering theory for Schrödinger operators with long-range potentials I, abstract theory, J. Math. Soc. Japan, 29 (1977), 665-691.
  4. Scattering theory for Schrödinger operators with long-range potentials II, spectral and scattering theory, J. Math. Soc. Japan, 30 (1978), 603-632.
  5. Asymptotic behavior of some oscillatory integrals, J. Math. Soc. Japan, 31 (1979), 127-140.
  6. Correction to "Asymptotic behavior of some oscillatory integrals", J. Math. Soc. Japan, 32 (1980), 781-782.
  7. On a construction of the fundamental solution for Schrödinger equations, J. Fac. Sci., The Univ. Tokyo, 27 (1980), 193-226.
  8. A family of Fourier integral operators and the fundamental solution for a Schrödinger equation, (with H. Kumano-go), Osaka J. Math., 18 (1981), 291-360.
  9. Scattering theory for Schrödinger equations with time-dependent potentials of long-range type, J. Fac. Sci., The Univ. Tokyo, 29 (1982), 353-369.
  10. A scattering theory for time-dependent long-range potentials, (with K. Yajima), Duke Math. J., 49 (1982), 341-376.
  11. A calculus of Fourier integral operators and the global fundamental solution for a Schrödinger equation, Osaka J. Math., 19 (1982), 863-900.
  12. Remarks on our paper "A scattering theory for time-dependent long-range potentials", (with K. Yajima), Duke Math. J., 50 (1983), 1005-1016.
  13. Bound states and scattering states for time periodic Hamiltonians, (with K. Yajima), Ann. Inst. H. Poincare, XXXIX (1983), 145-157.
  14. Time-decay of the high energy part of the solution for a Schrödinger equation, J. Fac. Sci., The Univ. Tokyo, 31 (1984), 109-146.
  15. Asymptotic behavior of the scattering amplitude at high energies, (with H. Isozaki), in "Differential Equations," ed. by I. W. Knowles & R. T. Lewis, North-Holland (1984), pp. 327-334.
  16. Micro-local resolvent estimates for 2-body Schrödinger operators, (with H. Isozaki), J. Funct. Anal., 57 (1984), 270-300.
  17. Modified wave operators with time-independent modifiers, (with H. Isozaki), J. Fac. Sci., The Univ. Tokyo, 32 (1985), 77-104.
  18. A remark on the micro-local resolvent estimates for two-body Schrödinger operators, (with H. Isozaki), Publ. RIMS, Kyoto Univ., 21 (1985), 889-910.
  19. Scattering matrices for two-body Schrödinger operators, (with H. Isozaki), Sci. Papers of the Coll. Arts & Sci., The Univ. Tokyo, 35 (1985), 81-107. (http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/21174/1/scp035005.pdf , http://repository.dl.itc.u-tokyo.ac.jp/dspace/handle/2261/21174 , http://jairo.nii.ac.jp/0021/00011589 )
  20. A relation between the modified wave operators W_J^{+-} and W_D^{+-}, Sci. Papers of the Coll. Arts & Sci., The Univ. Tokyo, 36 (1986), 91-105.
  21. Fourier integral operators with weighted symbols and micro-local resolvent estimates, J. Math. Soc. Japan, 39 (1987), 455-476.
  22. Scattering theory in quantum mechanics, Sugaku (Mathematics), 39, 1987, 159-167 (In Japanese).
  23. Fundamental solutions and eigenfunction expansions for Schrödinger operators, I. Fundamental solutions, Math. Z., 198 (1988), 181-190.
  24. Fundamental solutions and eigenfunction expansions for Schrödinger operators, II. Eigenfunction expansions, (with A. Jensen), Math. Z., 199 (1988), 1-13.
  25. Fundamental solutions and eigenfunction expansions for Schrödinger operators, III. Complex potentials, Sci. Papers Coll. Arts & Sci., The Univ. of Tokyo, 39 (1989), 109-123.
  26. Asymptotic completeness of N-body wave operators, I. Short-range quantum systems, Rev. in Math. Phys. 3 (1991), 101-124.
  27. Asymptotic completeness of N-body wave operators, II. A new proof for the short-range case and the asymptotic clustering for long-range systems, in "Functional Analysis and Related Topics, 1991," ed. H. Komatsu, Lect. Note in Math. 1540, Springer-Verlag, 1993, pp.149-189.
  28. Quantum theory of scattering -- From Kato school to Enss, Sigal, Suri-Kagaku (Mathematical Sciences), No. 347, May 1992 (In Japanese).
  29. N-body scattering and chaos -- classical and quantum theory (N体散乱とカオス-古典論と量子論), Bussei Kenkyu Vol. 59, No.6 (19930320) pp. 812-827 (In Japanese. 物性研究刊行会 ISSN:05252997 基研短期研究会 「保存力学系カオスにおける古典論と量子論」, 研究会報告)
  30. Theory of local times, Il Nuovo Cimento, 109 B (1994), No. 3, 281-302 (http://arxiv.org/abs/astro-ph/9309051).
  31. Theory of local times II. Another formulation and examples (http://xxx.lanl.gov/abs/gr-qc/9403007) (1994).
  32. Local time and the unification of physics Part I. Local time, (with L. Fletcher), Apeiron, 3 (1996), No. 2, 38-45 (http://arxiv.org/abs/gr-qc/0110065).
  33. What are Mathematical Sciences, Suri-Kagaku (Mathematical Sciences), No. 398, August 1996 (In Japanese), pp. 63--74.
  34. Quantum mechanics and relativity --- Their unification by local time --- in "Spectral and Scattering Theory," ed. A. G. Ramm, Plenum Press, New York, 1998, pp.39-66. (gr-qc/9612043)
  35. Comments on the Problem of Time --- A response to "A Possible Solution to the Problem of Time in Quantum Cosmology" by Stuart Kauffman and Lee Smolin, (with L. Fletcher) (gr-qc/9708055) (1997).
  36. A possible solution for the non-existence of time, (gr-qc/9910081) (1999).
  37. Quantum mechanical time contradicts the uncertainty principle, (gr-qc/9911060) (1999).
  38. Scattering Spaces and a Decomposition of Continuous Spectral Subspace of N-body Quantum Systems, (http://xxx.lanl.gov/abs/math.SP/9912244) (2000).
  39. Three dimensional time and energy operators and an uncertainty relation, (quant-ph/0007028) (2000).
  40. Quantum Mechanical Clock and Classical Relativistic Clock, (gr-qc/0102057) (2001).
  41. Local Time and the Unification of Physics Part II. Local System, (gr-qc/0110066) (2001).
  42. Locality and the Universe, International Conference on "time," "KitadaTime," Interaction and Communication - Trinity, Canada, August 28 - 31, 2002 at Ceta-Research, Trinity, Newfoundland, Canada, keynote speech, (2002).
  43. Time is just an auxiliary parameter, (2002).
  44. Rhythm Based Time and the conventional time, (2002).
  45. Inconsistent Universe -- Physics as a meta-science --, (http://arXiv.org/abs/physics/0212092) (2002).
  46. Is mathematics consistent?, (http://arXiv.org/abs/math.GM/0306007) (2003).
  47. Does Church-Kleene ordinal $\omega_1^{CK}$ exist?, (http://arXiv.org/abs/math.GM/0307090) (2003).
  48. Quantum Mechanics, Lectures in Mathematical Sciences, vol. 23, The University of Tokyo, 2005, x + 168 pp. ISSN 0919-8180, ISBN 1-000-01896-2. (http://arxiv.org/abs/quant-ph/0410061)
  49. Introduction to Mathematics for Scientists (理学を志す人のための数学入門), (with T. Ono), Gendai-Suugaku-Sha (現代数学社), February 14, 2006, viii + 494 pp. ISBN 4-7687-0358-5. (正誤表).
  50. Fundamental solution global in time for a class of Schrödinger equations with time-dependent potentials, Communications in Mathematical Analysis 1 (2006), 137-147 (http://arxiv.org/abs/math.AP/0607101)
  51. A Story of Fourier Analysis 1 - 12 (フーリエ解析の話 1 - 12), Mathematics for Scientists (理系への数学) vol. 39, No. 6 - vol. 40, No. 5, Gendai-Suugaku-Sha (現代数学社), June, 2006 - May, 2007, ISSN 1344-1345.
  52. A Story of Fourier Analysis (フーリエ解析の話), Gendai-Suugaku-Sha (現代数学社), November 1, 2007, viii + 371 pp. ISBN 978-4-7687-0377-9. (正誤表)
  53. Gödel's Incompleteness Theorem 1 - 12 (ゲーデルの不完全性定理 1 - 12), Mathematics for Scientists (理系への数学) vol. 41, No. 4 - vol. 42, No. 3, Gendai-Suugaku-Sha (現代数学社), April, 2008 - March, 2009, ISSN 1344-1345.
  54. An implication of Gödel's incompleteness theorem, International Journal of Pure and Applied Mathematics, 52 (2009), No. 4, 511-567 (http://www.ijpam.eu/contents/2009-52-4/6/6.pdf).
  55. Asymptotically outgoing and incoming spaces and quantum scattering, Commun. Math. Anal. 8 (2010), No. 1, 12-25 (http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.cma/1270646491&view=body&content-type=pdf_1).
  56. Scattering theory for the fractional power of negative Laplacian, J. Abstr. Differ. Equ. Appl., 1 (2010), No. 1, 1-26 (http://math-res-pub.org/jadea/1/1/scattering-theory-fractional-power-negative-laplacian).
  57. A remark on simple scattering theory, Commun. Math. Anal. 11 (2011), No. 2, 124-138 (http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.cma/1298669958&view=body&content-type=pdf_1).
  58. A story of Lebesgue integral 1-10 (ルベーグ積分の話 1-10), Mathematics for Scientists (理系への数学) vol. 43, No. 7 - vol. 44, No. 4, Gendai-Suugaku-Sha (現代数学社), July, 2010 - April, 2011, ISSN 1344-1345.
  59. Rebuttal to the review of my paper “An implication of Gödel's incompleteness theorem” appeared in Zentralblatt für Mathematik, International Journal of Pure and Applied Mathematics, 70 (2011), No. 1, 11-14 (http://www.ijpam.eu/contents/2011-70-1/2/2.pdf).
  60. Gödel, A way toward the Discovery of the Incompleteness (ゲーデル 不完全性発見への道), Gendai-Suugaku-Sha (現代数学社), May 16, 2011, vi + 180 pp. ISBN 978-4-7687-0391-5.
  61. An implication of Gödel's incompleteness theorem II: Not referring to the validity of oneself's assertion, Commun. Math. Anal. 10 (2011), No. 2, 24-52 (http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.cma/1322489163&view=body\&content-type=pdf_1).
  62. Timeless system, superluminal phenomena, dark matter and big bang, International Journal of Mathematical Sciences, 11 (2012), No. 1-2, Jan.-June 2012, 141-151. (http://www.metasciences.ac/time_XV.pdf)
  63. Introduction to Mathematical Analysis (数理解析学概論), Gendai-Suugaku-Sha (現代数学社), Oct. 7, 2012, x + 591, ISBN 978-4-7687-0407-3.
  64. Wave operators and similarity for long range N-body Schrödinger operators, Commun. Math. Anal. 19 (2016), No. 1, 6-66 (http://arxiv.org/abs/1511.05137).
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