Application of the functional calculus to solving of infinite dimensional heat equation

Abstract

In this paper we study infinite dimensional heat equation associated with the Gross Laplacian. Using the functional calculus method, we obtain the solution of appropriate Cauchy problem in the space of polynomial ultradifferentiable functions. The semigroup approach is considered as well.

Algebraic and differential properties of polynomial Fourier transformation

“…A new approach, that applies the theory of locally convex tensor products together with techniques on symmetric tensor products, is proposed in the papers [5,9] in order to obtain different polynomial extensions of spaces of ultradifferentiable functions and ultradistributions. In such spaces it is possible to construct a functional calculus for functions of infinity many variables [14] and to solve some Cauchy problems, for example, infinite dimensional heat equation associated with the Gross Laplacian [13].…”