Author/Authors :
Arefijamaal، A.A. نويسنده 1Department of Pure Mathematics, Faculty of Mathematics and Computer Sciences, , , Kamyabi Gol، RA نويسنده , , Raisi Tousi، R. نويسنده Department of Pure Mathematics , , Tavallaei، N. نويسنده 3Department of Pure Mathematics, School of Mathematics and Computer Science, DamghanUniversity, Damghan, Islamic Republic of Iran ,
Abstract :
This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a continuous Riesz basis. Finally we find a measure with respect to which, a continuous wavelet frame is a continuous Riesz basis.
