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Exponential function of pseudodifferential operator of minimum type

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초록

We show that an exponential function of a pseudodifferential operator of minimum type can be defined as a pseudodifferential operator of product type in a natural manner. We prepare the preliminary process which is necessary for such a definition and provide an exponential law with the aid of the definition.

Abstract

We show that an exponential function of a pseudodifferential operator of minimum type can be defined as a pseudodifferential operator of product type in a natural manner. We prepare the preliminary process which is necessary for such a definition and provide an exponential law with the aid of the definition.

참고문헌 (14)

  1. Aoki, T, "Calcul exponentiel des op´erateurs microdiff´erentiels d’ordre infini. I", Ann. Inst. Fourier, Grenoble, 33(4), pp.227~250 (1983)
  2. Aoki, T, "Symbols and formal symbols of pseudodifferential operators, Advanced Syudies in Pure Math", pp.181~208 (1984), Oxford
  3. Aoki, T, "Exponential calculus of pseudodifferential operators", Sˆugaku, 35(4), pp.302~315 (1983)
  4. Aoki, T, "The exponential calculus of microdifferential operators of infinite order III", Japan Acad. Ser. A math Sci, 59(3,), pp.79~82 (1983)
  5. Aoki, T, "The exponential calculus of microdifferential operators of infinite order II", Proc. Japan Acad. Ser. A Math . Sci, 58(4), pp.154~157 (1982)
  6. Aoki, T, "The exponential calculus of microdifferential operators of infinite order I", Proc. Japan Acad. Ser. A Math . Sci, 58(2), pp.58~61 (1982)
  7. Aoki, T, "The theory of symbols of pseudodifferential operators with infinite order, Lectures in Mathematical Sciences" (1997), Univ. of Tokyo
  8. Aoki, T, "Invertibility for microdifferential operators of Infinite Order", pp.1~29 (1982), RIMS, Kyoto Univ
  9. Kataoka,K, "On the theory of Radon transformations of hyperfunctions and its applications", 석사, pp.1976
  10. Kataoka, K, "On the theory of hyperfunctions", J. Fac. Sci. Univ. Tokyo Sect. IA, 28, pp.331~412 (1981)
  11. Kataoka, K, "Microlocal energy methods and pseudo-differential operators", Invent. math, 81, pp.305~340 (1985)
  12. 이창훈, "Composition of pseudodifferential operators of product type", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 12(3), pp.289~298 (2009), 장전수학회
  13. Lee, C. H, "Further results of composition in exponential calculus of pseudodifferential operators of minimum type", The Journal of Korea Naval Academy, 51, pp.339~350 (2008)
  14. Sato, M, "Microfunctions and Pseudodifferential Equations, Hyperfunctions and Pseudo Differential Equations", pp.265~529 (1973), Springer

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