Geodesic
On extension theorems in spaces of infinitely differentiable functions
Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 375-389 
G. S. Balashova. On extension theorems in spaces of infinitely differentiable functions. Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 375-389. http://geodesic.mathdoc.fr/item/SM_1983_46_3_a3/
@article{SM_1983_46_3_a3,
     author = {G. S. Balashova},
     title = {On extension theorems in spaces of infinitely differentiable functions},
     journal = {Sbornik. Mathematics},
     pages = {375--389},
     year = {1983},
     volume = {46},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_46_3_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions on a sequence $\{f_\omega(x)\}$ of functions sufficient for there to exist an extension in the space $$ W^\infty\{a_\alpha,p,r\}\equiv\biggl\{u(x)\in C^\infty(G),\quad\rho(u)\equiv\sum_{|\alpha|=0}^\infty a_\alpha\|D^\alpha u\|_r^p <\infty\biggr\} $$ are established in the one-dimensional case $G\equiv(a,b)$ and also in the multidimensional strip $G\equiv\mathbf R^\nu\times[a, b]$. The conditions obtained reduce matters to a study of convergence of numerical series, and in a number of cases are not only sufficient but also necessary. Bibliography: 9 titles.

[1] Dubinskii Yu. A., “Prostranstva Soboleva beskonechnogo poryadka i povedenie reshenii nekotorykh kraevykh zadach pri neogranichennom vozrastanii poryadka uravneniya”, Matem. sb., 98 (140) (1975), 163–184 | MR | Zbl

[2] Dubinskii Yu. A., “O sledakh funktsii v prostranstvakh Soboleva beskonechnogo poryadka i neodnorodnykh kraevykh zadachakh”, DAN SSSR, 235:6 (1977), 1249–1252 | MR | Zbl

[3] Dubinskii Yu. A., “Sledy funktsii iz prostranstv Soboleva beskonechnogo poryadka i neodnorodnye zadachi dlya nelineinykh uravnenii”, Matem. sb., 106 (148) (1978), 66–84 | MR | Zbl

[4] Balashova G. S., “Nekotorye teoremy prodolzheniya v prostranstve Soboleva beskonechnogo poryadka i neodnorodnye kraevye zadachi”, DAN SSSR, 244:6 (1979), 1294–1297 | MR | Zbl

[5] Mandelbroit S., Primykayuschie ryady. Regulyarizatsiya posledovatelnostei. Primeneniya, IL, M., 1955

[6] Balashova G. S., “Netrivialnost nekotorogo klassa funktsii i razreshimost nelineinykh differentsialnykh uravnenii beskonechnogo poryadka”, Trudy MEI, 1978, no. 357, 11–12 | MR | Zbl

[7] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[8] Seeley R. T., “Extension of $C^\infty$ functions defined in half-space”, Proc. Amer. Math. Soc., 15 (1964), 625–626 | DOI | MR | Zbl

[9] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, t. II, Nauka, M., 1969