Extremal problems in nonquasianalytic Carleman classes. Applications

An extremal problem is considered in the family of functions in a nonquasianalytic Carleman class on a closed interval that vanish together with all derivatives at a point in this interval. Applications to approximation theory and, in particular, to a system of exponentials with exponents satisfying the Fejér (or Levinson) condition are indicated; an asymptotic estimate as $\delta\to 0$ is obtained for the distance in $C_{[0,\delta]}$ between a fixed exponential and the closure of the linear span of other elements of this system.
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