RUS  ENG
Full version
JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. Akad. Nauk SSSR Ser. Mat., 1987 Volume 51, Issue 6, Pages 1292–1308 (Mi im1341)

This article is cited in 3 papers

On the extension of infinitely differentiable functions

G. S. Balashova


Abstract: Conditions on logarithmically convex sequences $\{M_n\}$ and $\{\widehat M_n\}$ are obtained under which, for every sequence $\{b_n\}$ with $|b_n|<C_1^nM_n$, $n=0,1,2,\dots$, there exists an infinitely differentiable function $f(x)$ such that $f_{(0)}^{(n)}=b_n$ and $\|f^{(n)}\|_{L_p(R)}\leqslant C_2^n\widehat M_n(p)$, $1\leqslant p\leqslant\infty$.
Bibliography: 17 titles.

UDC: 517.946.9

MSC: Primary 26E10; Secondary 40A99

Received: 09.12.1985


 English version:
Mathematics of the USSR-Izvestiya, 1988, 31:3, 603–620

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025