Balashova, G. S. Some classes of infinitely differentiable functions. (English) Zbl 0936.26012 Math. Bohem. 124, No. 2-3, 167-172 (1999). Summary: For nonquasianalytic Carleman classes conditions on the sequences \(\{\widehat {M}_n\}\) and \(\{M_n\}\) are investigated which guarantee the existence of a function in \(C_J\{\widehat {M}_n\}\) such that \[ u^{(n)}(a) = b_n, \quad |b_n|\leq K^{n+1} M_n, \quad n = 0,1,\dots , \quad a\in J. \] Conditions of coincidence of the sequences \(\{\widehat {M}_n\}\) and \(\{M_n\}\) are analysed. Some still unknown classes of such sequences are pointed out and a construction of the required function is suggested. The connection of this classical problem with the problem of the existence of a function with given trace at the boundary of the domain in a Sobolev space of infinite order is shown. MSC: 26E10 \(C^\infty\)-functions, quasi-analytic functions 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:Carleman class; Sobolev space PDF BibTeX XML Cite \textit{G. S. Balashova}, Math. Bohem. 124, No. 2--3, 167--172 (1999; Zbl 0936.26012) Full Text: EuDML OpenURL