The author suggests a method of characterizing of the kernel of a convolution-type operator. The method is based on the exact description of nontrivial expansions of zero of an absolutely representing system consisting of eigen vectors of some linear operator with continuous spectrum. The method suggested in the paper is applied to the characterization of the kernel of the convolution-type operator defined on some space of entire functions and to the factorization of such an operator.
KOROBEINIK, Yu. F. (1996) "ABSOLUTELY REPRESENTING SYSTEMS AND CONVOLUTION OPERATORS IN THE COMPLEX DOMAIN," Turkish Journal of Mathematics: Vol. 20: No. 2, Article 11. Available at: https://journals.tubitak.gov.tr/math/vol20/iss2/11