A differential equation theoretic interpretation of a geometric result of Hartogs
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- by Takahiro Kawai PDF
- Proc. Amer. Math. Soc. 98 (1986), 222-224 Request permission
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
- S. Bochner, Partial differential equations and analytic continuations, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 227–230. MR 50119, DOI 10.1073/pnas.38.3.227
- Leon Ehrenpreis, A new proof and an extension of Hartogs’ theorem, Bull. Amer. Math. Soc. 67 (1961), 507–509. MR 131663, DOI 10.1090/S0002-9904-1961-10661-7
- Leon Ehrenpreis, Fourier analysis in several complex variables, Pure and Applied Mathematics, Vol. XVII, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1970. MR 0285849
- F. Hartogs, Über die aus den singulären Stellen einer analytischen Funktion mehrerer Veränderlichen bestehenden Gebilde, Acta Math. 32 (1909), no. 1, 57–79 (German). MR 1555046, DOI 10.1007/BF02403211 S. Hitotumatu, The theory of analytic functions of several complex variables, Baifukan, Tokyo, 1960. (Japanese)
- Takahiro Kawai, Extension of solutions of systems of linear differential equations, Publ. Res. Inst. Math. Sci. 12 (1976/1977), no. 1, 215–227. MR 0415687, DOI 10.2977/prims/1195190964
- Mikio Sato, Takahiro Kawai, and Masaki Kashiwara, Microfunctions and pseudo-differential equations, Hyperfunctions and pseudo-differential equations (Proc. Conf., Katata, 1971; dedicated to the memory of André Martineau), Lecture Notes in Math., Vol. 287, Springer, Berlin, 1973, pp. 265–529. MR 0420735
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 222-224
- MSC: Primary 32D99
- DOI: https://doi.org/10.1090/S0002-9939-1986-0854023-1
- MathSciNet review: 854023