On the eigenproblem for convolution integral equations

Summary This paper concerns the eigenproblem for convolution integral equations whose kernels can be expressed as finite or infinite Fourier transforms of integrable functions. A procedure which closely parallels previous work on displacement integral equations is derived and the problem of existence is treated. Approximations are obtained for both the eigenvalues and the eigenfunctions.The results of this paper are taken from the author's doctoral dissertation at the University of New Mexico. The research was supported by the United States Atomic Energy Commission.