The paper defines and studies a property of functions of several complex variables analytic at the origin which is called local hyperbolicity with respect to a given real direction. For homogeneous polynomials it reduces to ordinary hyperbolicity. Local hyperbolicity is also extended so as to correspond to the hyperbolicity of nonhomogeneous polynomials.
KeywordsMain Lemma Newton Polygon Compact Part Impure Version Hyperbolic Polynomial
Unable to display preview. Download preview PDF.
- 1.K. G. Andersson,Propagation of analyticity of solutions of partial differential equations with constant coefficients, Ark. Mat.8 (27) (1971).Google Scholar
- 4.H. Komatsu,A local version of Bochner’s tube theorem (1972), to appear in J. Fac. Sci. Univ. Tokyo, Sect I, A.Google Scholar
- 5.S. Lojasiewicz,Ensembles semi-analytiques, Mimeographed notes. IHES (1967).Google Scholar
- 6.J. Milnor,Singular Point of Complex Hypersurfaces, Princeton, 1968.Google Scholar
- 7.R. Narasimhan,Introduction to Analytic Spaces, Springer Lecture Notes in Mathematics, 1966.Google Scholar
- 8.S. Leif Svensson,Necessary and sufficient conditions for the hyperbolicity of polynomials with hyperbolic principal part, Ark. Mat.8 (17) (1969).Google Scholar