Extension and lacunas of solutions of linear partial differential equations
Annales de l'Institut Fourier, Volume 46 (1996) no. 2, p. 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.
@article{AIF_1996__46_2_429_0,
     author = {Franken, Uwe and Meise, Reinhold},
     title = {Extension and lacunas of solutions of linear partial differential equations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {46},
     number = {2},
     year = {1996},
     pages = {429-464},
     doi = {10.5802/aif.1520},
     zbl = {0853.35022},
     mrnumber = {97h:35005},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1996__46_2_429_0}
}
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://www.numdam.org/item/AIF_1996__46_2_429_0/

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