ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 26, 35, 46 Balashova, Galina, Moscow Power Engineering Institute, Russia Some classes of infinitely differentiable functions For nonquasianalytical Carleman classes conditions on the sequences {M̂_{n}} and {M_{n}} are investigated which guarantee the existence of a function in C_{J}{M̂_{n}} that u^{(n)}(a) = b_{n}, |b_{n}| ≤ K^{n+1}M_{n}, n = 0, 1, ..., a ∈ J. Conditions for the coincidence of the sequences {M̂_{n}} and {M_{n}} are analyzed. Some still unknown classes of such sequences are indicated and the construction of the required function is suggested. The problem of the existence of a function in the space W^{∞}{a_{α}, p}_{(G)} with a given trace at the boundary is considered. Moreover, conditions for the existence of a function from the space for a one-dimensional domain and a multidimensional strip are obtained. In some cases the derived sufficient conditions for the trace extension are necessary as well. The construction method of the required function is described.