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A differential equation theoretic interpretation of a geometric result of Hartogs

Author: Takahiro Kawai
Journal: Proc. Amer. Math. Soc. 98 (1986), 222-224
MSC: Primary 32D99
MathSciNet review: 854023
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Abstract: A result of Hartogs on the location of singularities of holomorphic functions can be neatly proved by the theory of overdetermined systems of linear differential equations.

References [Enhancements On Off] (What's this?)

  • [1] S. Bochner, Partial differential equations and analytic continuations, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 227-230. MR 0050119 (14:279a)
  • [2] L. Ehrenpreis, A new proof and an extension of Hartogs' theorem, Bull. Amer. Math. Soc. 67 (1961) 507-509. MR 0131663 (24:A1511)
  • [3] -, Fourier analysis in several complex variables, Wiley-Interscience, New York, London, Sydney, Toronto, 1970. MR 0285849 (44:3066)
  • [4] F. Hartogs, Über die aus den singulären Stellen einer analytischen Funktion mehrerer Veränderlichen bestehenden Gebilde, Acta Math. 32 (1909), 57-79. MR 1555046
  • [5] S. Hitotumatu, The theory of analytic functions of several complex variables, Baifukan, Tokyo, 1960. (Japanese)
  • [6] T. Kawai, Extension of solutions of systems of linear differential equations, Publ. Res. Inst. Math. Sci. Kyoto Univ. 12 (1976), 215-227. MR 0415687 (54:3767)
  • [7] M. Sato, T. Kawai, and M. Kashiwara, Microfunctions and pseudo-differential equations, Lecture Notes in Math., vol. 287, Springer-Verlag, Berlin, New York, Heidelberg, 1973, pp. 265-529. MR 0420735 (54:8747)

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Keywords: Removable singularities, domain of holomorphy, system of linear differential equations, characteristic variety, characteristic
Article copyright: © Copyright 1986 American Mathematical Society

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