Open Access

# Continuous frame in Hilbert spaces

### Abstract

In this paper we introduce a mean of a continuous frame which is a generalization of discrete frames. Since a discrete frame is a special case of these frames, we expect that some of the results that occur in the frame theory will be generalized to these frames. For such a generalization, after giving some basic results and theorems about these frames, we discuss the following: dual to these frames, perturbation of continuous frames and robustness of these frames to an erasure of some elements.

### Article Information

 Title Continuous frame in Hilbert spaces Source Methods Funct. Anal. Topology, Vol. 12 (2006), no. 2, 170-182 MathSciNet MR2238038 Copyright The Author(s) 2006 (CC BY-SA)

### Authors Information

A. Rahimi
Department of Mathematics, Tabriz University, Tabriz, Iran

A. Najati
Department of Mathematics, Tabriz University, Tabriz, Iran

Y. N. Dehghan
Department of Mathematics, Tabriz University, Tabriz, Iran

### Citation Example

A. Rahimi, A. Najati, and Y. N. Dehghan, Continuous frame in Hilbert spaces, Methods Funct. Anal. Topology 12 (2006), no. 2, 170-182.

### BibTex

@article {MFAT336,
AUTHOR = {Rahimi, A. and Najati, A. and Dehghan, Y. N.},
TITLE = {Continuous frame in Hilbert spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {12},
YEAR = {2006},
NUMBER = {2},
PAGES = {170-182},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=336},
}