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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.


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Article Information

TitleContinuous frame in Hilbert spaces
SourceMethods Funct. Anal. Topology, Vol. 12 (2006), no. 2, 170-182
MathSciNet MR2238038
CopyrightThe 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 


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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},
}


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