2006/03/28 by Palle E. T. Jørgensen, Jorgensen, Palle E. T.
Computer Science · Engineering · #33C50 #42C15 #46E22 #47B32 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.math/0603661
openalex publication_date 2006/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building on a geometric formula for the analysis operator defined from F. Our focus is on the infinite-dimensional case where a priori estimates play a central role, and we extend a number of results which are known so far only in finite dimensions. We further show how this approach may be used both in constructing useful frames in analysis and in applications, and in understanding their geometry and their symmetries.