On continuous orthonormal bases

The orthogonality of the members of given orthonormal basis in Hilbert spaces playing the central role in the study of R-duals of frames.In the generalization and extension ofthe concept R-dual to continuous frames, we need to the defnition of continuous orthonormal basis but in available defnitions the orthogonality condition is not mentioned and cannot be obtained from the previous assumptions. To solve this problem, we present a new defnition. Using this defnition, we defned R-dual of continuous Bessel mappings.

Keywords:

frame , continuous frame , Riesz dual