# Some classes of infinitely differentiable functions

Mathematica Bohemica (1999)

- Volume: 124, Issue: 2-3, page 167-172
- ISSN: 0862-7959

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topBalashova, G. S.. "Some classes of infinitely differentiable functions." Mathematica Bohemica 124.2-3 (1999): 167-172. <http://eudml.org/doc/248459>.

@article{Balashova1999,

abstract = {For nonquasianalytical Carleman classes conditions on the sequences $\lbrace \widehat\{M\}_n\rbrace $ and $\lbrace M_n\rbrace $ are investigated which guarantee the existence of a function in $C_J\lbrace \widehat\{M\}_n\rbrace $ such that
u(n)(a) = bn, bnKn+1Mn, n = 0,1,..., aJ.
Conditions of coincidence of the sequences $\lbrace \widehat\{M\}_n\rbrace $ and $\lbrace M_n\rbrace $ 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.},

author = {Balashova, G. S.},

journal = {Mathematica Bohemica},

keywords = {Carleman class; Sobolev space; Carleman class; Sobolev space},

language = {eng},

number = {2-3},

pages = {167-172},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Some classes of infinitely differentiable functions},

url = {http://eudml.org/doc/248459},

volume = {124},

year = {1999},

}

TY - JOUR

AU - Balashova, G. S.

TI - Some classes of infinitely differentiable functions

JO - Mathematica Bohemica

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 124

IS - 2-3

SP - 167

EP - 172

AB - For nonquasianalytical Carleman classes conditions on the sequences $\lbrace \widehat{M}_n\rbrace $ and $\lbrace M_n\rbrace $ are investigated which guarantee the existence of a function in $C_J\lbrace \widehat{M}_n\rbrace $ such that
u(n)(a) = bn, bnKn+1Mn, n = 0,1,..., aJ.
Conditions of coincidence of the sequences $\lbrace \widehat{M}_n\rbrace $ and $\lbrace M_n\rbrace $ 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.

LA - eng

KW - Carleman class; Sobolev space; Carleman class; Sobolev space

UR - http://eudml.org/doc/248459

ER -

## References

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- Balashova G. S., Conditions for the extension of a trace and an embedding for Banach spaces of infinitely differentiable functions, Mat. Sb. 184 (1993), no. 1, 105-128. (In Russian.) (1993) MR1211368
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