Complete families of solutions to the heat equation and generalized heat equation in n-dimensional real Euclidean spaces

Construction of a complete family of solutions for parabolic equations in three or more space variables is addressed. The simplest case of the heat equation in n space variables and a class of parabolic equations in n space variables with singular coefficients are treated. Recent results in the analytic theory of parabolic equations are invoked in the study. The analysis is presented as a contribution toward development of a more general theory for parabolic equations in three or more variables with variable coefficients.