Abel’s integral equation as a convolution transform

A Certain Integral-recurrence Equation with Discrete-continuous Auto-convolution

Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.

A one-dimensional symmetry result for solutions of an integral equation of convolution type∗

We consider an integral equation in the plane, in which the leading operator is of convolution type, and we prove that monotone (or stable) solutions are necessarily one-dimensional. Mathematics Subject Classification: 45A05, 47G10, 47B34.

A Convolution Equation on a Compact Interval

Spatial-domain Convolution/deconvolution Transform

A new linear transform is deened for real valued functions which can be expanded in Taylor series. For an image which can be expressed by the Taylor expansion of a function, the new transform corresponds to convolution of the image with a point spread function. The point spread function must satisfy the condition that it's zero-th moment is non-zero and positive integer moments are nite. The fo...

An Efficient Method to Calculate the Convolution Based Reaction Integral Using the Analytical Fourier Transform

A major step in the numerical solution of electromagnetic scattering problems involves the computation of the convolution based reaction integrals. In this paper a procedure based on the analytical Fourier transform is introduced which allows us to calculate the convolution-based reaction integrals in the spectral domain without evaluating any convolution products directly. A numerical evaluati...