2016/05/09 by К. С. Казарян, Kazarian, K. S.
Mathematics · #41A30 #41A63 #42C30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1605.02456
openalex publication_date 2016/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an element of the finitely generated shift-invariant subspace as a linear combination of Fourier transformations of generators. An estimate for the norms of those coefficients is derived. For the proof a sort of orthogonalization procedure for generators is used which reminds the well known Gram-Schmidt orthogonalization process.