University of TehranJournal of Sciences, Islamic Republic of Iran1016-110424120130301A New Approach to Continuous Riesz Bases636931924ENA.A.ArefijamaalDepartment of Pure Mathematics, Faculty of Mathematics and Computer Sciences,
HakimSabzevariUniversity, Sabzevar, Islamic Republic of IranR.A.Kamyabi GolDepartment of Pure Mathematics, School of Mathematical Sciences, Ferdowsi
University of Mashhad, Mashhad, Islamic Republic of IranR.Raisi TousiDepartment of Pure Mathematics, School of Mathematical Sciences, Ferdowsi
University of Mashhad, Mashhad, Islamic Republic of IranN.TavallaeiDepartment of Pure Mathematics, School of Mathematics and Computer
Science, DamghanUniversity, Damghan, Islamic Republic of IranJournal Article20120201This 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.https://jsciences.ut.ac.ir/article_31924_e476eb337f845777bb13757486bf7036.pdf