The fundamental operator functions of degenerate heat equations in Banach spaces

A generalized solution for the fundamental operator functions of degenerate heat equation in banach spaces is constructed. Methods of perturbation theory of linear operators, the semigroup of operators with kernels, and generalized functions and operations are used. It is sufficient to construct a fundamental operator function to solve a degenerate heat equation. The proof of certain theorems reduce to verifying the conditions in the definitions of a fundamental operator function and use properties of the pseudoinverse operator, relations between the elements of the Jordan sets of Fredholm operators and take into account the relation between the dimensions of the kernels.