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Journal of Function Spaces and Applications
Volume 2013, Article ID 163814, 7 pages
http://dx.doi.org/10.1155/2013/163814
Research Article

Construction of Frames for Shift-Invariant Spaces

1Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovica 4, 21000 Novi Sad, Serbia
2Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovića 12, 34000 Kragujevac, Serbia

Received 9 May 2013; Accepted 25 July 2013

Academic Editor: Satit Saejung

Copyright © 2013 Stevan Pilipović and Suzana Simić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We construct a sequence which constitutes a -frame for the weighted shift-invariant space , , and generates a closed shift-invariant subspace of . The first construction is obtained by choosing functions , , with compactly supported Fourier transforms , . The second construction, with compactly supported , gives the Riesz basis.