Approximation of the Muntz-Szasz Type in Weight Spaces L-p and Zeroes of Functions of Bergman Classes in a Half-Plane

We study the completeness of the system of exponents exp(-lambda(n)t), Re lambda(n) > 0, in spaces L-p with the power weight on the semiaxis R+. We prove a sufficient condition for the completeness; one can treat it as a modification of the well-known Szasz condition. With p = 2 it is unimprovable (in a sense). The proof is based on the results (which are also obtained in this paper) on the distribution of zeroes of functions of the Bergman classes in a half-plane.