Document Type : Original Paper
Authors
1 Department of Pure Mathematics, Faculty of Mathematics and Computer Sciences, HakimSabzevariUniversity, Sabzevar, Islamic Republic of Iran
2 Department of Pure Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
3 Department 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.
Keywords
)