On extension of infinitely differentiable functions. (Russian) Zbl 0643.26015

Balashova, G. S.

Izv. Akad. Nauk SSSR, Ser. Mat. 51, No. 6, 1292-1308 (1987).

In this paper the author is continuing the work on extension of infinitely differentiable functions, initiated by E. Borel in 1895. Among others she investigates extensions with estimations \(\max | f^{(n)}(x)|\) and \(\| f^{(n)}(x)\|_{L_ r(R)}\quad (1\leq r\leq \infty).\) Moreover, conditions for extensions of boundary conditions of inward domains in \(W^{\infty}\{a_ n,p,r\}_{(0,\alpha)}\) and in \(W^{\infty}\{a_{\tau},p,r\}_{(R^{\nu}\times (0,\alpha))}\) are presented. The obtained results are too involved to be reproduced here, so for details we have to refer to the paper.

Reviewer: J.Abrycht

MSC:

26E10	\(C^\infty\)-functions, quasi-analytic functions
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

extension of infinitely differentiable functions