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

S.V. Sharyn

doi:10.15330/cmp.8.2.313-322

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

Authors

S.V. Sharyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0003-2547-1442

https://doi.org/10.15330/cmp.8.2.313-322

Keywords:

infinite dimensional heat equation, Gross Laplacian, space of polynomial ultradifferentiable functions, space of polynomial ultradistributions

Published online: 2016-12-30

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.