Convolution and product in finitely generated shift-invariant spaces

2025/04/30 by Aleksandar Aksentijević, Aksentijević, Aleksandar, Suzana Aleksić +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2505.00197

openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss some structural properties of finitely generated shift-invariant (FGSI) spaces and subspaces of Sobolev spaces, particularly those related to convolution and the product within these spaces. We find shift-invariant solutions in FGSI spaces for a class of differential-difference equations with constant coefficients. Additionally, we analyze the Fourier multipliers in FGSI spaces and the wave fronts for the convolution and product in FGSI spaces.

Citations

• On the product of periodic distributions. Product in shift-invariant spaces
• Characterization of multilinear multipliers in terms of Sobolev space\n regularity
• Dynamical Sampling for Shift-preserving Operators
• Diagonalization of Shift-Preserving Operators
• Wave fronts via Fourier series coefficients
• Frames for weighted shift-invariant spaces
• Estimates for translation invariant operators in Lp spaces

Related

• Shift-invariant subspaces of Sobolev type
• On the structure of finitely generated shift-invariant subspaces
• Nearly invariant subspaces for operators in Hilbert spaces
• On the product of periodic distributions. Product in shift-invariant spaces
• Finite difference calculus in the continuum