The space of initial data of the 3d boundary-value problem for a parabolic differential-difference equation in the one-dimensional case.

The article discusses the space of the initial data of the three-dimensional (3D) boundary-value problem for a parabolic differential-difference equation. It says that linear bounded operators such as extension of a function by zero and the projectrion operator of a function into the interval were introduced. It mentions that the Sobolev space of complex-value was denoted.