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

Soient K⊂Q des ensembles compacts, convexes dans ℝ 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 ℰ(K) des fonctions C ∞ sur K au sens de Whitney a une extension comme zéro-solution dans ℰ(Q) ou dans ℰ(ℝ n ). Des caractérisations intéressantes sont une condition du type de Phragmén-Lindelöf sur la variété de P dans ℂ n et une condition pour des solutions élémentaires pour P(D) avec lacunes.

Let K⊂Q be compact, convex sets in ℝ 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 ℰ(K) of all C ∞ -functions on K extends to a zero solution in ℰ(Q) resp. in ℰ(ℝ n ). The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of P in ℂ n and in terms of fundamental solutions for P(D) with lacunas.

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     author = {Franken, Uwe and Meise, Reinhold},
     title = {Extension and lacunas of solutions of linear partial differential equations},
     journal = {Annales de l'Institut Fourier},
     pages = {429--464},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {46},
     number = {2},
     year = {1996},
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     mrnumber = {97h:35005},
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Franken, Uwe; Meise, Reinhold. Extension and lacunas of solutions of linear partial differential equations. Annales de l'Institut Fourier, Tome 46 (1996) no. 2, pp. 429-464. doi : 10.5802/aif.1520. https://aif.centre-mersenne.org/articles/10.5802/aif.1520/

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