Bu çalışmada bazı lineer operatörlerin özdeğerlerinden oluşan mutlak temsil sistemleri kullanılarak konvolosyon operatörlerinin çekirdekleri incelenmiş ve bunların bazı uygulamaları verilmiştir.

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.