Linear combinations of frame generators in systems of translates

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• 作者：C. Cabrelli ; C.A. Mosquera ; V. Paternostro
• 关键词：Shift invariant space ; Minimal generator set ; Finitely generated shift invariant space ; Frame ; Riesz basis ; Gramian
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：15 May, 2014
• 年：2014
• 卷：413
• 期：2
• 页码：776-788
• 全文大小：318 K

文摘

A finitely generated shift invariant space V is a closed subspace of that can be generated by the integer translates of a finite number of functions. A set of frame generators for V is a set of functions whose integer translates form a frame for V. In this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators. Surprisingly the results are very different from the recently studied case when the property to be a frame is not required.