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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.

### Article Information

 Title A new metric in the study of shift invariant subspaces of $L^2(\mathbb{R}^n)$ Source Methods Funct. Anal. Topology, Vol. 18 (2012), no. 3, 214-219 MathSciNet MR3051791 zbMATH 1265.46049 Copyright The 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

### 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},
}