Equivalent Condition to a Frame Sequence


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Authors

  • Uma Srivastava Department of Mathematics and Statistics, Deen Dayal Upadhyay University, Gorakhpur, Uttar Pradesh, India

Keywords:

Abelian Group, frame Sequence, Fourier transform, subgroup

Abstract

Let G be a second countable locally compact abelian group and H a countable closed discrete subgroup of G such that the quotient group G/H is compact. A simple proof of characterization of frame generated by a function $\phi \in L^{2}(G)$ and its translates by elements of H in terms of the boundedness of the periodization of its Fourier transform $\hat{\phi }$ is given.

 

Author Biography

Uma Srivastava, Department of Mathematics and Statistics, Deen Dayal Upadhyay University, Gorakhpur, Uttar Pradesh, India

 

 

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Published

12-02-2023

How to Cite

Uma Srivastava. (2023). Equivalent Condition to a Frame Sequence. International Journal of Mathematics And Its Applications, 11(1), 21–31. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/623

Issue

Section

Research Article