List of Research Works (English Version) (in the Published Order)

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1 List of Research Works (English Version) (in the Published Order) Yoshifumi Ito(*) March 3, 2019 Books, Original Papers and Papers of Proceedings and others 1. Theory of H-valued Fourier Hyperfunctions, Proc. Japan Acad., 51(7)(1975), , (joint work with Shigeaki Nagamachi), (published on ). 2. On the Theory of Vector Valued Fourier Hyperfunctions, J.Math.Tokushima Univ., 9(1975), 1-33, (joint work with Shigeaki Nagamachi), ( ). 3. A Note on One-parameter Semi-groups of -endomorphisms of C -algebras, J.Math.Tokushima Univ., 11(1977), 1-10, ( ). 4. Analytic Linear Mappings and Vector Valued Hyperfunctions, RIMS Kôkyûroku, 355(1979), , (1979.6), (in 5. On the Theory of Vector Valued Hyperfunctions, J.Math.Tokushima Univ., 13(1979), 29-51, ( ). 6. Introduction to Linear Algebra, Kyôritu, 1980, (in Japanese), (out of print). 7. Theory of Analytic Linear Mappings, I. General Theory, J.Math.Tokushima Univ., 14(1980), 25-74, ( ). 8. Analytic Linear Mappings and Vector Valued Hyperfunctions, J.Math.Tokushima Univ., 15(1981), 1-51, ( ). 9. On the Oka-Cartan-Kawai Theorem B for the Sheaf E Õ, Publ.RIMS.Kyoto Univ., 18(3)(1982), , ( ). 10. On the Abstract Cauchy Problems in the Sense of Fourier Hyperfunctions, J.Math.Tokushima Univ., 16(1982), 25-31, ( ). 11. Fourier Hyperfunction Semi-groups, J.Math.Tokushima Univ., 16(1982), 33-53, ( ). 12. Theory of (Vector Valued ) Fourier Hyperfunctions. Their Realization as Boundary Values of (Vector Valued ) Slowly Increasing Holomorphic Functions, (I), J.Math.Tokushima Univ., 18(1984), , ( ). 1

2 13. Theory of Hypo-probability Measures, RIMS Kôkyûroku, 558(1985), , (1985.4), (in 14. Theory of (Vector Valued ) Fourier Hyperfunctions. Their Realization as Boundary Values of (Vector Valued ) Slowly Increasing Holomorphic Functions, (II), J.Math.Tokushima Univ., 19(1985), 25-61, ( ). 15. Stationary Fourier Hyperprocesses, Publ.RIMS,Kyoto Univ., 22(1)(1986), 31-42, (1986.3). 16. Theory of (Vector Valued ) Sato Hyperfunctions. Their Realization as Boundary Values of (Vector Valued ) Holomorphic Functions, J.Math.Tokushima Univ., 20(1986), 27-39, ( ). 17. Linear Algebra, Kyôritu, ( ), (in 18. Fourier hyperfunctions of general type, J.Math.Kyoto Univ., 28(2)(1988), , (1988.7). (Thesis). 19. Fourier hyperfunctions of general type, RIMS Kôkyûroku, 704(1989), 18-27, ( ), (in 20. Theory of (Vector Valued ) Fourier Hyperfunctions. Their Realization as Boundary Values of (Vector Valued ) Slowly Increasing Holomorphic Functions, (III), J.Math.Tokushima Univ., 23(1989), 23-38, ( ). 21. Theory of Fourier Micro-functions, Proceedings of 1989 Real Analysis Seminar, pp , (1990), (in 22. Theory of (Vector Valued ) Fourier Hyperfunctions. Their Realization as Boundary Values of (Vector Valued ) Slowly Increasing Holomorphic Functions, (IV), J.Math.Tokushima Univ., 24(1990), 13-21, ( ). 23. Errata of Theory of (Vector Valued ) Fourier Hyperfunctions. Their Realization as Boundary Values of (Vector Valued ) Slowly Increasing Holomorphic Functions, (III), J.Math.Tokushima Univ., 23(1989),23-38, J.Math.Tokushima Univ., 24(1990), 23-24, ( ). 24. Analysis, Vol. I, Science House, ( ), (in 25. Mathematical Statistics, Science House, ( ), (in 26. Sato Hyperfunctions Valued in a Locally Convex Space, Proceedings of 1991 Real Analysis Seminar, pp.24-45, (1992), (in 27. Vector valued Fourier hyperfunctions, J.Math. Kyoto Univ., 32(2)(1992), , (1992.7). 28. Theory of General Fourier Hyperfunctions, Proceedings of 1992 Real Analysis Seminar, pp.16-30, (1993), (in 29. Theory of (Vector Valued ) Fourier Hyperfunctions. Their Realization as Boundary Values of (Vector Valued ) Slowly Increasing Holomorphic Functions, (V), J.Math.Tokushima Univ., 26(1992), 39-50, ( ). 30. L 2 -estimates and existence theorems for the exterior differential operators, Real Analysis Seminar 1993, pp.49-63, (1994). 31. On the Borel Graph Theorem and the Open Mapping Theorem, J. Math. Tokushima Univ., 27(1993), 17-21, ( ). 2

3 32. Boundary Values of (Slowly Increasing ) Holomorphic Functions, J. Math. Tokushima Univ., 27(1993), 23-35, ( ). 33. Stationary Fourier Hyperfields, J. Math. Tokushima Univ., 28(1994), 39-54, ( ). 34. Theory of Fourier Microfunctions of Several Types, (I), J. Math. Tokushima Univ., 29(1995), 55-75, ( ). 35. Theory of Fourier Microfunctions of Several Types, Proceedings of the Fourth International Colloquium on Finite or Infinite Dimensional Complex Analysis, pp.21-31, Kyushu Univ. Co-op, Fukuoka, Japan, (December 1996). 36. Theory of Fourier Microfunctions of Several Types, (II), J. Math. Tokushima Univ., 30(1996), 45-69, ( ). 37. Theory of Fourier Microfunctions of Several Types, (III), J. Math. Tokushima Univ., 31(1997), 29-61, ( ). 38. Analysis, Vol. II, Science House, ( ), (in (out of print). 39. Sato Hyperfunctions Valued in a Locally Convex Space, J. Math. Tokushima Univ., 32(1998), 27-41, ( ). 40. New Axiom of Quantum Mechanics Hilbert s 6th Problem, J. Math. Tokushima Univ., 32(1998), 43-51, ( ). 41. New Axiom of Quantum Mechanics Hilbert s 6th Problem, Real Analysis Symposium 1998, Takamatsu, pp , (1999). 42. Axioms of Arithmetic, Science House, ( ), (in (Reference: Iwanami Dictionary of Mathematics, 4th ed p.514). 43. L 2 -estimates and existence theorems for the exterior differential operators, J. Math. Tokushima Univ., 33(1999), 15-32, ( ). 44. Mathematical Principles of Quantum Mechanics. New Theory, Science House, ( ), (in 45. Sato Hyperfunctions Valued in a Locally Convex Space, Proceedings of the Second ISAAC Congress, Vol.I, pp , Kluwer Academic Publishers, Dortrecht/Boston/London, (2000). 46. New definition of products of distributions, J. Math. Tokushima Univ., 34(2000), 9-14, ( ). 47. Theory of Quantum Probability, J. Math. Tokushima Univ., 34(2000), 23-50, (2001.1). 48. New definition of products of distributions, Real Analysis Symposium 2000, Fukuoka, pp.46-51, (2001), (in 49. Theory of (Vector Valued ) Sato Hyperfunctions on a Real Analytic Manifold, J. Math. Univ. Tokushima, 35(2001), 17-33, (2002.1). 50. Methods of Renormalization and Distributions, J. Math. Univ. Tokushima, 35(2001), 35-55, ( ). 3

4 51. Variational Principles and Schrödinger Equations, Natural Science Research, Faculty of Integrated Arts and Sciences, The University of Tokushima, 15(2002), 1-7, (joint work with K. Kayama), ( ), (in Japanese). 52. Foundation of Analysis, Science House, ( ), (in 53. Variational Principles and Schrödinger Equations, RIMS Kôkyûroku, 1278(2002), 86-95, (joint work with K. Kayama), (in 54. Theory of Measure and Integration, Science House, ( ), (in 55. Analysis, Vol, II, (Rev. Ed. ), Science House, ( ), (in 56. New Quantum Theory and New Meanings of Planck s Radiation Formula, Natural Science Research, Faculty of Integrated Arts and Sciences, The University of Tokushima, 16(2003), 1-10, (in Japanese), (joint work with K. Kayama and Y. Kamosita), ( ). 57. Theory of General Fourier Hyperfunctions, J. Math. Univ. Tokushima, 36(2002), 7-34, ( ). 58. Theory of Infraexponential Holomorphic Functions, J. Math. Univ. Tokushima, 37(2003), 1-18, ( ). 59. New Quantum Theory. Present Situation and Problems, Real Analysis Symposium 2004, Osaka, pp , (2004). 60. New Notions of Convergence of Directed Families of Points and Convergence of Filters, J. Math. Univ. Tokushima, 38(2004), 9-16, ( ). 61. New Quantum Theory and New Meaning of Specific Heat of a Solid, J. Math. Univ. Tokushima, 38(2004), 17-27, (joint work with Md Sharif Uddin), ( ). 62. New Quantum Theory and New Meaning of Specific Heat of an Ideal Gas, J. Math. Univ. Tokushima, 38(2004), 29-40, (joint work with Md Sharif Uddin), ( ). 63. New Quantum Theory. Present Situation and Problems, Natural Science Research, Faculty of Integrated Arts and Sciences, The University of Tokushima, 18(2004), 1-14, ( ), (in 64. Why the area is obtained by the integration, Mathematics Seminar, , 44, no.6, pp.50-53, (in 65. Theory of infraexponenntial holomorphic functions, Proceedings of the 12th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, ed. by H. Kazama, M. Morimoto and C. -C. Yang, pp , Kyushu University Press, (2005). 66. The Fundamental Principles of New Quantum Theory, Natural Science Research, Faculty of Integrated Arts and Sciences, The University of Tokushima, 19(2005), 1-18, ( ), (in 67. Memorial of Retirement. Professor Yoshifumi Ito, Selected Papers by the Author, Department of Mathematical Sciences, Faculty of Integrated Arts and Sciences, The University of Tokushima, ( ). (not for sale). 68. New Quantum Theory, Vol. I, Science House, 2006, (in 4

5 69. Black Body Radiation and Planck s Law of Radiation, RIMS Kôkyûroku, 1482(2006), pp , RIMS, (RIMS Seminar on Applications of Renormalization Group at Mathematical Sciences, September 7 September 9, 2005, Organizer, Keiiti R. Ito). (in 70. Fundamental Principles of New Quantum Theory, Real Analysis Symposium 2006, Hirosaki, pp.25-28, (in 71. Solutions of Variational Problems and Derivation of Schrödinger Equations, Real Analysis Symposium 2006, Hirosaki, pp.29-32, (in 72. Yoshifumi Ito (shared writer), Iwanami Dictionary of Mathematics, 4th ed., edited by Mathematical Society of Japan, Iwanami Shoten, ( ), (in 73. Complex Analysis, Science House, (2007), (in 74. New Quantum Theory, Vol.II, Science House, (2007), (in 75. New Meanings of Conditional Convergence of the Integrals, Real Analysis Symposium 2007, Osaka, pp.41-44, (in 76. New Solutions of Some Variational Problems and the Derivation of Schrödinger Equations, Complex Analysis and its Applications, pp , OMUP(Osaka Municipal Universities Press), (March, 2008). (Proceedings of the 15th International Conference on Finite or Infinite Complex Analysis and Applications, July 30 August 3, 2007, Osaka City University, Eds., Yoichi Imayoshi, Yohei Komori, Masaharu Nishio, and Ken-ichi Sakan). 77. Vector Analysis, Science House, (2008), (in 78. What are Happening in the Physics of Electrons, Atoms and Molecules? Physical Reality Revisited, RIMS Kôkyûroku 1600, pp , Research Institute of Mathematical Sciences of Kyoto University, Kyoto, Japan, ( ). (Symposium at RIMS of Kyoto University, Applications of Renormalization Group Methods in Mathematical Sciences, September 12 September 14, 2007, Organizer, Keiichi R. Ito). 79. Potential Barrier and Tunnel Effect, Real Analysis Symposium 2008, Yamaguti, pp.67-70, (in 80. Fundamental Principles of Natural Statistical Physics, Science House, (2009), (in 81. On the Specific Heat of Black Body, Real Analysis Symposium 2009, Sakato, pp.35-40, (2010.1). 82. Differential Calculus of L p -functions and L p loc-functions, Real Analysis Symposium 2009, Sakato, pp , (2010.1). 83. Exercises of Vector Analysis, Science House, (2010), (in 84. Study on the New Axiomatic Method Giving the Solutions of Hilbert s 2nd and 6th Problems, J. Math. Univ. Tokushima, 44(2010), 1-12, ( ). 85. Definition and Existence Theorem of Jordan Measure, Real Analysis Symposium 2010, Kitakyushu, pp.1-4, ( ). 5

6 86. Definition of the Concept of Natural Numbers and its Existence Theorem. Solution of Hilbert s Second Problem, J. Math. Univ. Tokushima, 45(2011), 1-7, ( ). 87. Differential Calculus of L p -functions and L p loc-functions. Revisited, J. Math. Univ. Tokushima, 45(2011), 49-66, ( ). 88. Some aspects of natural statistical physics, Real Analysis Symposium 2011, Nagano, pp.18-24, ( ), (in 89. What is Probability? Real Analysis Symposium 2011, Nagano, pp.48-53, ( ), (in 90. Angular Momentum and its Expectation Value, RIMS Kôkyûroku 1805, pp.14-24, Research Institute of Mathematical Sciences of Kyoto University, Kyoto, Japan, (2012.8). (Symposium at RIMS of Kyoto University, Applications of Renormalization Group Methods in Mathematical Sciences, September 12 September 14, 2011, edited by K. R. Ito). 91. Study on the Phenomena of Potential Well in the View Point of Natural Statistical Physics, J. Math. Univ. Tokushima, 46(2012), Study on Systems of Hydrogen Atoms in the View Point of Natural Statistical Physics, J. Math. Univ. Tokushima, 46(2012), Corrections of the paper Definition of the Concept of Natural Numbers and its Existence Theorem. Solution of Hilbert s Second Problem, Published in J.Math. Univ. Tokushima, 45(2011), 1-7, J. Math. Univ. Tokushima, 46(2012), Fundamental Principles of Natural Statistical Physics, J. Math. Univ. Tokushima, 47(2013), Study on A. Tonomura s Experiment of Bi-prism of Electron Beam, J. Math. Univ. Tokushima, 47(2013), Fourier transformation of L 2 loc-functions and its applications, Real Analysis Symposium 2013, Okayama, pp.5-8, ( ), (in 97. Space-Time-Matter. Taward a New Understanding of Physical Phenomena, Real Analysis Symposium 2013, Okayama, pp.41-44, ( ), (in 98. Definition and Existence Theorem of the Concept of Ordinal Numbers, J. Math. Univ. Tokushima, 48(2014), 23-33, ( ). 99. Laws of Natural Statistical Physics, J. Math. Univ. Tokushima, 48(2014), 41-70, ( ) Spectral Measure and Spectral Integral, Real Analysis Symposium 2014, Toyama, pp.17-24, ( ) Sturm-Liouville s Eigenvalue Problem, Real Analysis Symposium 2014, Toyama, pp.55-62, ( ), (in 102. Fourier Transformation of L 2 loc-functions, J. Math. Tokushima Univ., 49(2015), 39-58, ( ) Study on the Phenomena of Potential Well of Infinite Depth on the View Point of Natural Statistical Physics, J. Math. Tokushima Univ., 49(2015), 59-77, ( ). 6

7 104. Study on the Phenomena of the System of Free Paricles on the View Point of Natural Statistical Physics, J. Math. Tokushima Univ., 49(2015),79-93, ( ) New Proof of Plancherel s Theorem, J. Math. Tokushima Univ., 50(2016),81-89, ( ) Development of L p -calculus, J. Math. Tokushima Univ., 50(2016),91-111, ( ) Fourier Transformation of Distributions, J. Math. Tokushima Univ., 50(2016), , ( ) Differentiation of Lebesgue-Stieltjes Measures, Real Analysis Symposium 2016, Nara, (in Japanese), pp ( ) Study on the relativity of motion, Real Analysis Symposium 2016, Nara,(in Japanese), pp ( ) Fourier Transformation of L p loc-functions, J. Math. Tokushima Univ., 51(2017), 55-70, ( ) Axiomatic Method of Measure and Integration (I). Definition and Existence Theorem of the Jordan Measure, J.Math. Tokushima Univ., 52(2018), 1-15, ( ) Axiomatic Method of Measure and Integration (II). Definition of the Riemann Integral and its Fundamental Properties, J.Math. Tokushima Univ., 52(2018), 17-38, ( ) Some problems on the Riemann Integral, Real Analysis Symposium 2018, Osaka, pp.1-6, ( ), (in 114. Definition of the Concept of Sets and its Existence Theorem, Real Analysis Symposium 2018, Osaka, pp.31-36, ( ), (in Japanease) Axiomatic Method of Measure and Integration (III). Definition and Existence Theorem of the Lebesgue Measure, submitted, ( ) Axiomatic Method of Measure and Integration (IV). Definition of the Lebesgue Integral and its Fundamental Properties, submitted, ( ). Preprints of Books, Original Papers and Papers of Proceedings and others 1. Hannnya Sinngyou with Commentary, preprint, ( ), (in 2. World of Mathematical Sciences, preprint, ( ), (in 3. Natural Statistical Physics, preprint, ( ), (in 4. Statistics, preprint, ( ), (in 5. Differential and Integral Calculus II, Theory of Riemann Integral, preprint, ( ), (in 6. Theory of Hyperfunctions, I, preprint, ( ), (in 7

8 7. Theory of Lebesgue Integral, preprint, ( ), (in 8. Differential and Integral Calculus, I, Theory of Differentiation, preprint, ( ), (in 9. Vector Analysis (Rev. Ed.), preprint, ( ), (in 10. Theory of Hyperfunctions, II, preprint, ( ), (in 11. Theory of Hyperfunctions, III, preprint, ( ), (in 12. RS-integral and LS-integral, preprint, ( ), (in 13. Theory of Function Spaces and Theory of Hyperfunctions, preprint, ( ), (in 14. Curve Integral and Surface Integral, preprint, ( ), (in 15. Principles of Natural Philosophy, preprint, ( ), (in 16. Foundation of Linear Algebra, preprint, ( ), (in 17. Philosophy of Buddhism, preprint, ( ), (in 18. Resume of Hannya Sutra, preprint, ( ), (in 19. Mathematical Foundations of Natural Statistical Physics, preprint, ( ), (in 20. Set and Topology, preprint, ( ), (in 21. Introduction to Analysis, preprint, ( ), (in 22. Fourier Analysis, preprint, ( ), (in 23. Japanese Translation, Hannya Sinngyou, preprint, ( ), (in 24. The Teachings of Buddhism, preprint, ( ), (in 25. Wonderful Fountain (Human Beings, I), preprint, ( ), (in 26. Wonderful Fountain (Human Beings, II), preprint, ( ), (in 27. Sutra of Nyoze Party, preprint, ( ), (in 28. Foundation of Mathematical Statistics, preprint, ( ), (in 29. Foundation of Natural Statistical Physics, preprint, ( ), (in 30. Wonderful Fountain (Natural Sciences, I), preprint, ( ), (in 31. Axiomatic Method of Measure and Integration (V). Definition and Existence Theorem of the RS-measure, preprint, ( ), (in 32. Axiomatic Method of Measure and Integration (VI). Definition of the RS-integral and its Fundamental Properties, preprint, ( ), (in 33. Axiomatic Method of Measure and Integration (VII). Definition and Existence Theorem of the LS-measure, preprint, ( ), (in 34. Axiomatic Method of Measure and Integration (VIII). Definition of the LS-integral and its Fundamental Properties, preprint, ( ), (in 8

9 35. Axiomatic Method of Measure and Integration (IX). Definition of the R-type Curve Integral and its Fundamental Properties, preprint, ( ), (in 36. Axiomatic Method of Measure and Integration (X). Definition of the L-type Curve Integral and its Fundamental Properties, preprint, ( ), (in 37. Axiomatic Method of Measure and Integration (XI). Definition of the R-type Surface Integral and its Fundamental Properties, preprint, ( ), (in 38. Axiomatic Method of Measure and Integration (XII). Definition of the L-type Surface Integral and its Fundamental Properties, preprint, ( ), (in 39. Axiomatic Method of Measure and Integration (XIII). Definition of the R-type Higher Dimensional Surface Integral and the L-type Higher Dimensional Surface Integral, preprint, ( ), (in 40. Analysis of the Lebesgue Space, preprint, ( ), (in 41. On the Space-Time-Matter (1), preprint, ( ), (in 42. Spectral Analysis, preprint, ( ), (in 43. On the Space-Time-Matter (2), preprint, ( ), (in 44. On the Space-Time-Matter (3), preprint, ( ), (in 45. On the Space-Time-Matter (4), preprint, ( ), (in 46. On the Space-Time-Matter (5), preprint, ( ), (in 47. On the Space-Time-Matter (6), preprint, ( ), (in 48. Theory of Sato-Furier Hyperfunctions I, preprint. ( ). 49. On the Space-Time-Matter (7), preprint, ( ), (in 50. Definition of the Concept of Sets and its Existence Theorem, preprint, ( ), (in 51. On the Space-Time-Matter (8), preprint, ( ), (in 52. Space Time Matter, preprint, ( ), (Book in 53. Theory of Sato-Furier Hyperfunctions II, preprint. ( ). 54. Theory of Sato-Furier Hyperfunctions III, preprint. ( ). 55. Study on the Spectra of Ions of Hydrogen Type, preprint, ( ), (in 56. Limit of Sequence, preprint, , (in 57. Integral Calculus of Elementary Functions, preprint, , (in 58. Axiomatic Method of Measure and Integration (XIV). Cases of Measure and Integration on a Riemann Manifold, preprint, , (in 59. Life as Buddist I, preprint, , (in 60. Life as Buddist II, preprint, , (in 9

10 61. Theory of Sato-Furier Hyperfunctions IV, in preprint. ( ). 62. Foundation of Natural Statistical Physics, in preparation, (English Edition). 63. Theory of Differential Equations, in preparation, (in 64. Wonderful Fountain (Mathematics, I), (in 65. Wonderful Fountain (Human Beings, III), (in 66. Wonderful Fountain (Natural Sciences, II), (in 10

11 Problems to be considered 1. Analysis, Vol.I, (rev. ed.), , (in 2. Analysis, Vol.II, (3rd. ed.), , (in 3. Axiomatic Method of Measure and Integration (XVI). In the Case of Surface Area. Existence Theorem 4. On Rutherford s Scattering Formula 5. Structure of Atoms. 6. Higher Dimensinal Vector Analysys. 7. Introduction to Hyperfunctions of One Variable, to be appeared 8. Theory of Cohomology, to be appeared 9. Theory of Integral Equations, to be appeared 10. Theory of Variation, to be appeared 11. Theory of Classical Dynamics, to be appeared 12. Theory of Electro-Magnetics, to be appeared 13. Theory of Thermostatistical Dynamics, to be appeared 14. Theory of Relativity, to be appeared 15. Study on the Integration of Hyperfunctions Calculation of the Definite Integral by the Method of Cauchy. 17. Study on the Relation of the Class of Functions and the Topology. (*)Yoshifumi Ito (Professor Emeritus of the University of Tokushima, Doctor of Science) ; itoyoshifumi@fd5.so-net.ne.jp 11