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.

Keywords

• infinite dimensional heat equation
• gross laplacian
• space of polynomial ultradifferentiable functions
• space of polynomial ultradistributions