Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. G. Andersson,Propagation of analyticity of solutions of partial differential equations with constant coefficients, Ark. Mat.8 (27) (1971).
M. F. Atiyah, R. Bott, and L. Gårding,Lacunas for hyperbolic differential operators with constant coefficients I, Acta Math.124 (1970), 109–189; II. In preparation.
J. M. Bony and P. Schapira,Existence et prolongment des solutions analytiques des systèmes hyperboliques non stricts, C. R.274 (1972), 86–89.
H. Komatsu,A local version of Bochner’s tube theorem (1972), to appear in J. Fac. Sci. Univ. Tokyo, Sect I, A.
S. Lojasiewicz,Ensembles semi-analytiques, Mimeographed notes. IHES (1967).
J. Milnor,Singular Point of Complex Hypersurfaces, Princeton, 1968.
R. Narasimhan,Introduction to Analytic Spaces, Springer Lecture Notes in Mathematics, 1966.
S. Leif Svensson,Necessary and sufficient conditions for the hyperbolicity of polynomials with hyperbolic principal part, Ark. Mat.8 (17) (1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gårding, L. Local hyperbolicity. Israel J. Math. 13, 65–81 (1972). https://doi.org/10.1007/BF02760230
Issue Date:
DOI: https://doi.org/10.1007/BF02760230