| Abstract: | LetF ⊂ ℂ be a dense-in-itself set that has a nonempty connected interior and contains the origin, and let  be the space of infinitely differentiable complex-valued functions onF. For some classes of such setsF, we prove that for an arbitrary sequence  of complex numbers there exists a functionf ε  withf (n)(0)=d n,n=0, 1, 2, ..., and study the analyticity properties off. The functionf is constructed in the form of various function series, namely, a power series, a series of simple fractions, and an exponential series. Analytic solutions of the multidimensional Borel problem are also considered. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 525–538, April, 2000. |
