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Regularization and compression of integral operator kernels with tensor paraproducts
Abstract
We present a new perspective on integral operator kernels given by a nonlinear function of the distance. This perspective is useful since it permits one to quasilinearize the nonlinear transformations acting on the tensor Haar expansion of the distance, d(x,y). This leads to a new representation comprised of a principal and residual term with desirable features; namely, enhanced local regularity of the principal component (and in certain situations rapid off-diagonal decay leading to O(N) storage) and a residual expansion of improved approximation as a consequence of enhanced global regularity. Numerical experiments on the potential kernel are included
Related
- Weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels
- Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels
- Improving the accuracy of the Lorentz Integral Transform method using complex kernels
- Weighted Hp−Lq boundedness of integral operators with rough kernels
- Exact Finite Integral Geometry: Directional Kernels and Spherical Designs
BibTeX
@misc{fasina2026regularization,
title = {{Regularization and compression of integral operator kernels with tensor paraproducts}},
author = {Oluwadamilola Fasina and Ronald R. Coifman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15822},
eprint = {2609.15822},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15822},
}
RIS
TY - UNPB
TI - Regularization and compression of integral operator kernels with tensor paraproducts
AU - Oluwadamilola Fasina
AU - Ronald R. Coifman
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15822
UR - https://arxiv.org/abs/2609.15822
AB - We present a new perspective on integral operator kernels given by a nonlinear function of the distance. This perspective is useful since it permits one to quasilinearize the nonlinear transformations acting on the tensor Haar expansion of the distance, d(x,y). This leads to a new representation comprised of a principal and residual term with desirable features; namely, enhanced local regularity of the principal component (and in certain situations rapid off-diagonal decay leading to O(N) storage) and a residual expansion of improved approximation as a consequence of enhanced global regularity. Numerical experiments on the potential kernel are included
ER -