| Title:
|
Some classes of infinitely differentiable functions (English) |
| Author:
|
Balashova, G. S. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
167-172 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Carleman class |
| Keyword:
|
Sobolev space |
| MSC:
|
26E10 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 0936.26012 |
| idMR:
|
MR1780689 |
| DOI:
|
10.21136/MB.1999.126256 |
| . |
| Date available:
|
2009-09-24T21:36:40Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126256 |
| . |
| Reference:
|
[1] Mandelbroit S.: Adjoining Series. Regularization of Sequences. Applications.Izdat. Inostrannoj Literatury, Moskva, 1995. (In Russian.) |
| Reference:
|
[2] Bang T: On quasi-analytiske funktioner.Thèse, København, 1946. |
| Reference:
|
[3] Borel E.: Sur les fonctions d'une variable réelle indéfiniment dérivables.C.R. Acad. Sci. 174 (1922). |
| Reference:
|
[4] Carleman T.: Les fonctions quasi-analytiques.Paris, 1926. |
| Reference:
|
[5] Carleson L.: On universal moment problems.Math. Scand. 9 (1961), no. 2, 197-206. Zbl 0114.05903, MR 0142012, 10.7146/math.scand.a-10635 |
| Reference:
|
[6] Wahde G.: Interpolation on non-quasi-analytic classes of infinitely differentiable functions.Math. Scand. 20 (1967), no. 1, 19-31. MR 0214976, 10.7146/math.scand.a-10815 |
| Reference:
|
[7] Mitiagin B.S.: On infinitely differentiable function with the values of its derivates given at a point.Dokl. Akad. Nauk SSSR 138 (1961), 289-292. MR 0130946 |
| Reference:
|
[8] Ehrenpreis L.: The punctual and local images of quasi-analytic and non-quasi-analytic classes.Institute for Advanced Study, Princeton, N. J., 1961. Mimeographed. |
| Reference:
|
[9] Balashova G. S.: On extension of infinitely differentiable functions.Izv. Akad. Nauk SSSR, Ser. Mat. 51 (1987), no. 6, 1292-1308. (In Russian.) Zbl 0643.26015, MR 0933965 |
| Reference:
|
[10] 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.) MR 1211368 |
| Reference:
|
[11] Dubinskij Yu. A.: Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations.Mat. Sb. 106 (148) (1978), no. 1, 66-84. (In Russian.) Zbl 0414.35028 |
| . |
