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Symbols of Minimum Type and of Zero Class in Exponential Calculus

이창훈
영남수학회 (Youngnam Mathematical Society)|2018.01|East Asian Mathematical Journal|제34권 제1호|pp. 29-37|DOI http://dx.doi.org/10.7858/eamj.2018.004

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참고문헌

키워드

Exponential calculusPseudodifferential operatorSymbol.
주제분류수학

초록

We introduce formal symbols of product type, of zero class, and of minimum type and show that the formal power series representa- tions for ep and eq are formal symbols of product type giving the same pseudodifferential operator, where p and q are formal symbols of minimum type and p − q is of zero class.

Abstract

We introduce formal symbols of product type, of zero class, and of minimum type and show that the formal power series representa- tions for ep and eq are formal symbols of product type giving the same pseudodifferential operator, where p and q are formal symbols of minimum type and p − q is of zero class.

참고문헌 (17)

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  3. Aoki, T., "Exponential calculus of pseudodifferential operators(Japanese)", Sugaku, 35(4), pp.302~315 (1983)
  4. Aoki, T., "The exponential calculus of microdi erential operators of in nite order III", Proc. Japan Acad. Ser. A math Sci., 59(3), pp.79~82 (1983)[DOI]
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  8. Aoki, T., "Invertibility for microdifferential operators of In nite Order", Publ. RIMS, Kyoto Univ., 18, pp.1~29 (1982)[DOI]
  9. Kataoka, K., "On the theory of Radon transformations of hyperfunctions and its applications", 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)[DOI]
  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., "Exponential function of pseudodi erential operator of minimum type", Proceedings of the Jangjeon Mathematical Society, 14(1), pp.149~160 (2011)
  14. Lee, C. H., "The exponential calculus of pseudodi erential operators of minimum type. I", Proceedings of the Japan Academy, 89(1), pp.6~10 (2013)[DOI]
  15. C. H. Lee, "Formal adjoint of pseudodifferential operator of product type", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 17(2), pp.299~305 (2014), 장전수학회
  16. 이창훈, "A ROLE OF SYMBOLS OF MINIMUM TYPE IN EXPONENTIAL CALCULUS", East Asian Mathematical Journal, 32(1), pp.35~41 (2016), 영남수학회[DOI]
  17. Sato, M., "Microfunctions and Pseudodifferential Equations, Hyperfunctions and Pseudo-Differential Equations", Proceeding, Katata 1971, Lecture Notes in Math., 287, pp.265~529 (1973)

관련 논문AI추천

Exponential function of pseudodifferential operator of minimum type이창훈장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제1호Composition of pseudodifferential operators of product typeC. H. Lee장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제4호Composition of pseudodifferential operators of product type이창훈장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2009 · 제12권 제3호A ROLE OF SYMBOLS OF MINIMUM TYPE IN EXPONENTIAL CALCULUS이창훈영남수학회 · East Asian Mathematical Journal2016 · 제32권 제1호Asymptotic expansions of the solutions to the heat equations with hyperfunctions initial valueKunio Yoshino, Yasuyuki Oka대한수학회 · 대한수학회논문집2008 · 제23권 제4호On the commutant of multiplication operators with analytic polynomial symbolsB. Khani Robati대한수학회 · 대한수학회보2007 · 제44권 제4호

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