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http://dx.doi.org/10.7858/eamj.2016.004

A ROLE OF SYMBOLS OF MINIMUM TYPE IN EXPONENTIAL CALCULUS  

LEE, Chang Hoon (Department of Mathematics, Korea Naval Academy)
Publication Information
East Asian mathematical journal / v.32, no.1, 2016 , pp. 35-41 More about this Journal
Abstract
We introduce formal symbols of product type and of minimum type and show that the formal power series representation for $e^p$ is a formal symbol of product type, where p is a formal symbol of minimum type.
Keywords
Exponential calculus; Pseudodifferential operator; Symbol;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 Aoki, T.(1983). Calcul exponentiel des operateurs microdifferentiels d'ordre infini. I, Ann. Inst. Fourier, Grenoble, v. 33-4, pp. 227-250.   DOI
2 Aoki, T.(1984). Symbols and formal symbols of pseudodifferential operators, Advanced Syudies in Pure Math., v. 4 (K.Okamoto, ed.), Group Representation and Systems of Differential Equations, Proceedings Tokyo 1982, Kinokuniya, Tokyo; North-Holland, Amsterdam-New York-Oxford, pp. 181-208 .
3 Aoki, T.(1983). Exponential calculus of pseudodifferential operators(Japanese), Sugaku , v. 35, no. 4, pp. 302-315.
4 Aoki, T.(1983). The exponential calculus of microdifferential operators of infinite order III, Proc. Japan Acad. Ser. A math Sci., v. 59, no. 3, pp. 79-82.   DOI
5 Aoki, T.(1982). The exponential calculus of microdifferential operators of infinite order II, Proc. Japan Acad. Ser. A Math . Sci., v. 58, no. 4, pp. 154-157.   DOI
6 Aoki, T.(1982). The exponential calculus of microdifferential operators of infinite order I, Proc. Japan Acad. Ser. A Math . Sci., v. 58, no. 2, pp. 58-61.   DOI
7 Aoki, T.(1997). The theory of symbols of pseudodifferential operators with infinite order, Lectures in Mathematical Sciences (Japanese), Univ. of Tokyo, v. 14.
8 Aoki, T.(1982). Invertibility for microdifferential operators of Infinite Order, Publ. RIMS, Kyoto Univ., v. 18, pp. 1-29.   DOI
9 Kataoka, K.(1976). On the theory of Radon transformations of hyperfunctions and its applications, Master's thesis in Univ. Tokyo(Japanese).
10 Kataoka, K.(1981). On the theory of hyperfunctions, J. Fac. Sci. Univ. Tokyo Sect. IA, v. 28, pp. 331-412.
11 Kataoka, K.(1985). Microlocal energy methods and pseudo-differential operators, Invent. math., v. 81, pp. 305-340.   DOI
12 Lee, C. H.(2009). Composition of pseudodifferential operators of product type, Proceedings of the Jangjeon Mathematical Society, v. 12, no. 3, pp. 289-298.
13 Lee, C. H.(2011). Exponential function of pseudodifferential operator of minimum type, Proceedings of the Jangjeon Mathematical Society, v. 14, no. 1, pp. 149-160.
14 Lee, C. H.(2013). The exponential calculus of pseudodifferential operators of minimum type. I, Proceedings of the Japan Academy , v. 89, Ser. A, no. 1, pp. 6-10.   DOI
15 Lee, C. H.(2014). Formal adjoint of pseudodifferential operator of product type, Proceedings of the Jangjeon Mathematical Society, v. 17, no. 2, pp. 299-305.
16 Sato, M., T. Kawai and M. Kashiwara(1973). Microfunctions and Pseudodifferential Equations, Hyperfunctions and Pseudo-Differential Equations (H.Komatsu, ed.), Proceeding, Katata 1971, Lecture Notes in Math., v. 287, Springer, Berlin-Heidelberg-New York, pp. 265-529.