Integral transform methods: a critical review of various kernels

TL;DR

This paper critically reviews integral transform methods, emphasizing their advantages in calculating continuum response functions and exploring wavelet kernels through a model study.

Contribution

It provides a comprehensive critique of various kernels used in integral transforms, highlighting the potential of wavelets for response function calculations.

Findings

Wavelet kernels enable efficient matrix diagonalization for response calculations.

Integral transform methods are advantageous for continuum energy response analysis.

Wavelets show promise in model studies for response function computation.

Abstract

Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow calculations of the transform by matrix diagonalization. A particular set of such kernels, namely the wavelets, is tested in a model study.