Reproducing Kernels of Weight Square-Summable Sequences Hilbert Spaces

Abstract

In this paper we will introduce the concept of weighted reproducing kernel of l2(ℂ) space, in similiar way as it is done in case of weighted reproducing kernel of Bergman space. We will give an explicit formula for it and prove that it depends analytically on weight. In addition, we will show some theorems about dependance of l2(ℂ) space on weight.

Keywords

• reproducing kernel
• Hilbert space
• square-summable sequences
• 46E22