A representation theory for solutions of a higher order heat equation. I (Q1206830)

For the higher order heat equation given by \(\partial u/\partial t=(-1) ^{q+1} \partial^{2q}u/\partial t^{2q}\) (\(q\in N\)) the source solution \(G_ q(x,t)\) is studied. Among the properties which the authors study for \(G_ q(x,t)\) there are a useful estimate for \(G_ q(x,t)\) and its derivatives. Besides a set of polynomial solutions of the considered equation and their associated ones is defined and a variety of properties, including their relationship to some hypergeometric series and to generalized Hermite polynomials and their associated ones is derived, too. For part II see the following review.