Extension and lacunas of solutions of linear partial differential equations
Annales de l'Institut Fourier, Volume 46 (1996) no. 2, pp. 429-464.

Let KQ be compact, convex sets in n with K and let P(D) be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of P(D) in the space (K) of all C -functions on K extends to a zero solution in (Q) resp. in ( n ). The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of P in n and in terms of fundamental solutions for P(D) with lacunas.

Soient KQ des ensembles compacts, convexes dans n tel que K et soit P(D) un opérateur linéaire aux dérivées partielles à coefficients constants. On donne plusieurs conditions qui sont équivalentes au fait que chaque zéro-solution de P(D) dans l’espace (K) des fonctions C sur K au sens de Whitney a une extension comme zéro-solution dans (Q) ou dans ( n ). Des caractérisations intéressantes sont une condition du type de Phragmén-Lindelöf sur la variété de P dans n et une condition pour des solutions élémentaires pour P(D) avec lacunes.

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Franken, Uwe; Meise, Reinhold. Extension and lacunas of solutions of linear partial differential equations. Annales de l'Institut Fourier, Volume 46 (1996) no. 2, pp. 429-464. doi : 10.5802/aif.1520. http://archive.numdam.org/articles/10.5802/aif.1520/

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