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.

Full Text

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},
  MRNUMBER = {MR2238038},
       URL = {http://mfat.imath.kiev.ua/article/?id=336},
}