Geodesic
Some classes of infinitely differentiable functions
Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 167-172

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MR Zbl
For nonquasianalytical 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\vert b_n\vert\le 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.
For nonquasianalytical 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\vert b_n\vert\le 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.
DOI : 10.21136/MB.1999.126256
Classification : 26E10, 46E35
Keywords: Carleman class; Sobolev space 
Balashova, G. S. Some classes of infinitely differentiable functions. Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 167-172. doi: 10.21136/MB.1999.126256
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