Abstract
A necessary and sufficient condition is given for extension of real analytic solutions of P(D)u = 0 in a situation analogous to Hartogs’s theorem in several complex variables. It is expressed in terms of a Phragmén-Lindelöf type principle on N(P).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramczuk, W.: ‘On continuation of quasi-analytic solutions of partial differential equations to compact convex sets,’ J. Austral. Math. Soc. 39 (1985), 306–316.
Grusin, V.V.: ‘On solutions with isolated singularities for partial differential equations with constant coefficients’, Trans. Moscow Math. Soc. 15 (1966), 262–278.
Kaneko, A.: ‘Prolongement des solutions régulières de l’équation aux dérivées partielles à coefficients constants’, Séminaire Goulaouic-Schwartz 1976–7, Ecole Polytech., Paris, 1977, Exposé No.18.
Kaneko, A.: ‘On continuation of regular solutions of partial differential equations to compact convex sets II’, J. Fac. Sci. Univ. Tokyo Sec. 1A 18 (1972), 415–433.
Kaneko, A.: ‘On Hartogs type continuation theorem for regular solutions of linear partial differential equations with constant coefficients’, J. Fac. Sci. Univ. Tokyo Sec. 1A 35 (1988), 1–26.
Kaneko, A.: ‘On continuation of regular solutions of partial differential equations with constant coefficients’, J. Math. Soc. Japan 26 (1974), 92–123.
Kaneko, A.: ‘On continuation of real analytic solutions of linear partial differential equations’, Astérisque 89–90, Soc. Math. France, 1981, pp. 11–44.
Kawai, T.: ‘On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients’, J. Fac. Sci. Univ. Tokyo Sec. 1A 17 (1970), 467–517.
Palamodov, V.P.: Linear Differential Equations with Constant Coefficients, Moscow, 1967 (in Russian; English translation from Springer, 1970).
Polking, J.C.: ‘A survey of removable singularities’, Seminar on non-linear partial differential equations, Ed. by S.S. Chern, Springer, 1984, pp.261–292.
Saburi, Y.: ‘Fundamental properties of modified Fourier hyperfunctions’, Tokyo J. Math. 8 (1985), 231–273.
Tajima, S.: ‘Analyse microlocale sur les variétés de Cauchy-Riemann et problème du prolongement des solutions holomorphes des équations aux dérivées partielles’, Publ. RIMS Kyoto Univ. 18 (1982), 911–945.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Kluwer Academic Publishers
About this chapter
Cite this chapter
Kaneko, A. (1989). Hartogs Type Extension Theorem of Real Analytic Solutions of Linear Partial Differential Equations with Constant Coefficients. In: Terzioñlu, T. (eds) Advances in the Theory of Fréchet Spaces. NATO ASI Series, vol 287. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2456-7_5
Download citation
DOI: https://doi.org/10.1007/978-94-009-2456-7_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7608-1
Online ISBN: 978-94-009-2456-7
eBook Packages: Springer Book Archive