On some stability results of frame atomic decompositions

2005/02/10 by Massimo Fornasier, Fornasier, Massimo
Mathematics · #42C15 #46B99 #46H99 #65D99 #65J05 #65T60 #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.math/0502205

openalex publication_date 2005/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper is concerned with the implications of sufficient conditions ensuring that a perturbation of a frame is again a frame. We emphasize how stability of frames is fundamental for numerical applications and we discuss in particular the connection between stability conditions and localization principles for frame atomic decompositions in Banach spaces.

Citations

• The wavelet transform, time-frequency localization and signal analysis

Related

• Additive Stability of Frames
• Approximative K-Atomic Decompositions and frames in Banach Spaces
• Perturbations of frames
• Perturbation of Schauder frames and besselian Schauder frames in Banach spaces
• Upper and lower estimates for schauder frames and atomic decompositions