# Interpolation and Semi-group on Hilbert and Hardy Spaces of Dirichlet Series Ali Mohamed Abu Oam

**Abstract:** We investigate that a bounded sequence of points in the half plane $\sigma > \frac{1}{2}$ is an interpolating sequence for Hilbert space of ordinary Dirichlet series with square summable coefficiens. Also, in the half plane $\sigma > \frac{1}{2}$ we discuss the wold decomposition for the shift semi group on the Hardy space of square summable Dirichlet series. The local behavior of Hilbert space of Dirichlet series is considered, relative to the functions spaces on the infinite dimensional polydisk, and we generate some results for each case.

**Keyword:** Interpolating sequence,Hilbert and Hardy spaces, Dirichlet series and infinite dimensional polydisk.

**How to cite this article:**

Ali Mohamed Abu Oam, Interpolation and Semi-group on Hilbert and Hardy Spaces of Dirichlet Series, International Journal of Advances in Mathematics, Volume 2018, Number 3, Pages 66-80, 2018.