To investigate the singularity of the Newton integral kernel, the surface integration domain [[OMEGA].
Therefore, the Newton integral kernel is only weakly singular [Kellogg, 1929; Martinec, 1998]
Note that if [Lambda] is bounded then, formally, T has an integral kernel which is O([[absolute value of]x - y.
is an integral operator whose integral kernel has a mild singularity along the diagonal.
We replace g by [absolute value of g] and majorize S with an operator with a positive integral kernel which pointwise dominates the modulus of the kernel for S.
More precisely, bounds on the Fourier transform of the HDAF integral kernel show that it converges almost-uniformly to the ideal window, and that the pass and transition bands can be tuned independently to any width while preserving Gaussian decay in both time and frequency domains.
HDAF integral kernel is defined by Hoffman and other  as
In addition, we derive an asymptotic approximation formula for the HDAF integral kernel that shows its relation to a windowed sinc function, also referred to as Gaussian sinc-DAF by Hoffman and others (see  or ).
Local Zeta Regularization and the Scalar Casimir Effect: A General Approach Based on Integral Kernels
Their topics include the zeta-regularized stress-energy vacuum expectation value in terms of integral kernels, total energy and forces on the boundary, a massless field between parallel hyperplanes, a massive field constrained by perpendicular hyperplanes, and a scalar field with a harmonic background potential.
Dunkl, Integral kernels
with reflection group invariance, Canad.
An analysis of the integral kernels
for two well-known fan beam CT reconstruction algorithms has been performed.