%0 Journal Article
%T The Fourier transform and convolutions generated by a differential operator with boundary condition on a segment
%A Baltabek Kanguzhin
%A Niyaz Tokmagambetov
%J Mathematics
%D 2013
%I arXiv
%X We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution explicitly depends on the boundary condition that defines the domain of the operator $L.$ The convolution is closely connected to the inverse operator or to the resolvent. So, we first find a representation for the resolvent, and then introduce the required convolution.
%U http://arxiv.org/abs/1302.1262v1