Uncertainty Principles in Finitely generated Shift-Invariant Spaces with additional invariance

2011/11/16 by Romain Tessera, Tessera, Romain, Haichao Wang +1
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.FA

paper · pdf · doi:10.48550/arxiv.1111.3990

12 pages

openalex publication_date 2011/11/16 · arxiv created 2012/09/25 · arxiv updated 2012/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider finitely generated shift-invariant spaces (SIS) with additional invariance in L²(\R^d). We prove that if the generators and their translates form a frame, then they must satisfy some stringent restrictions on their behavior at infinity. Part of this work (non-trivially) generalizes recent results obtained in the special case of a principal shift-invariant spaces in L²(\R) whose generator and its translates form a Riesz basis.

Related

• Invariance of a Shift-Invariant Space in Several Variables
• Construction of frames for shift-invariant spaces
• Frames of translates with prescribed fine structure in shift invariant\n spaces
• p-Riesz bases in quasi shift invariant spaces
• Linear combinations of frame generators in systems of translates