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.

Full Text

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},
}