Riesz bases by replacement

In this paper we provide a method for constructing new Riesz bases on separable Hilbert spaces and we use it to prove sufficient conditions for the existence of exponential Riesz bases on domains of Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathbb {R}} }<^>d$$\end{document}. We also apply our results to the construction of weighted exponential Riesz bases on [0, 1].