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arXiv · 2505.00197

Convolution and product in finitely generated shift-invariant spaces

Aleksandar Aksentijević·Suzana Aleksić·Stevan Pilipović
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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.

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Aleksandar Aksentijević, Suzana Aleksić, Stevan Pilipović. 2025-04-30. Convolution and product in finitely generated shift-invariant spaces. https://arxiv.org/abs/2505.00197

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