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A new metric in the study of shift invariant subspaces of $L^2(\mathbb{R}^n)$


Abstract

A new metric on the set of all shift invariant subspaces of $L^2(\mathbb{R}^n)$ is defined and the properties are studied. The limit of a sequence of principal shift invariant subspaces under this metric is principal shift invariant is proved. Also, the uniform convergence of a sequence of local trace functions is characterized in terms of convergence under this new metric.


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Article Information

TitleA new metric in the study of shift invariant subspaces of $L^2(\mathbb{R}^n)$
SourceMethods Funct. Anal. Topology, Vol. 18 (2012), no. 3, 214-219
MathSciNet MR3051791
zbMATH 1265.46049
CopyrightThe Author(s) 2012 (CC BY-SA)

Authors Information

M. S. Balasubramani
Department of Mathematics, University of Calicut, Kerala, India

V. K. Harish
Thunchan Memorial Govt. College, Tirur, Kerala, India 


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Citation Example

M. S. Balasubramani and V. K. Harish, A new metric in the study of shift invariant subspaces of $L^2(\mathbb{R}^n)$, Methods Funct. Anal. Topology 18 (2012), no. 3, 214-219.


BibTex

@article {MFAT615,
    AUTHOR = {Balasubramani, M. S. and Harish, V. K.},
     TITLE = {A new metric in the study of shift invariant subspaces of $L^2(\mathbb{R}^n)$},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {18},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {214-219},
      ISSN = {1029-3531},
  MRNUMBER = {MR3051791},
 ZBLNUMBER = {1265.46049},
       URL = {http://mfat.imath.kiev.ua/article/?id=615},
}


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