Integral-kernel convolution formalism for mixed Hodge modules

Develop a convolution formalism for mixed Hodge modules by defining integral kernels in the mixed Hodge module setting, enabling the D’Agnolo–Eastwood style kernel-based comparison between Radon and Fourier–Laplace transforms to be carried out directly within the category of mixed Hodge modules.

Background

In comparing Radon and Fourier–Laplace transforms, D’Agnolo–Eastwood [DE03] used convolution via integral kernels. The present paper avoids convolution because the authors currently lack a framework for integral kernels in the mixed Hodge module category, and instead rely on other tools (notably Theorem 1.3) to achieve the comparison.

Establishing a kernel-based convolution theory for mixed Hodge modules would unify methodologies and potentially streamline such comparisons.