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A New Approach to Continuous Riesz Bases | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 6، دوره 24، شماره 1، خرداد 2013، صفحه 63-69 اصل مقاله (458.01 K) | ||
| نوع مقاله: Original Paper | ||
| نویسندگان | ||
| A.A. Arefijamaal1؛ R.A. Kamyabi Gol2؛ R. Raisi Tousi2؛ N. Tavallaei3 | ||
| 1Department of Pure Mathematics, Faculty of Mathematics and Computer Sciences, HakimSabzevariUniversity, Sabzevar, Islamic Republic of Iran | ||
| 2Department of Pure Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran | ||
| 3Department of Pure Mathematics, School of Mathematics and Computer Science, DamghanUniversity, Damghan, Islamic Republic of Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Continuous frame؛ Continuous orthonormal basis؛ Continuous Riesz basis | ||
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