1998/11/24 by Peter G. Casazza, Casazza, Peter G.
Mathematics · Neuroscience · #46B20 #46C05 #Algebra over a field #Arithmetic #Axon Guidance and Neuronal Signaling #Computer science #FOS: Mathematics #Frame (networking) #Functional Analysis (math.FA) #Mathematics #Orthonormal basis #Physics #Pure mathematics #Rings, Modules, and Algebras #Telecommunications #math.FA #msc:46B20 #msc:46C05
paper · pdf · doi:10.48550/arxiv.math/9811148
published in arXiv (Cornell University) (Cornell University) · to appear: J. of Fourier Anal. and Appl's
arxiv created 1998/11/24 · openalex publication_date 1998/11/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. A result of N.J. Kalton is included which shows that this is best possible in that: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two normalized tight frames or as a sum of an orthonormal basis and a Riesz basis for H. Finally, every frame can be represented as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.