Removable singular points of solutions of the laplace equation on hilbert space

Abstract

In this article one considers the Laplace operator on Hilbert space. This operator maps cylindrical measure on Hilbert space into a functional on sampling functions. In this case the set of sampling functions is the class of smooth cylindrical functions. If the measure is Σ-additive, then sampling functions can be not only cylindrical. For the Laplace equation one considers the fundamental solution and Dirichlet problem in a domain in Hilbert space. The first fundamental solution was constructed by L. Gross. This solution is the measure on Hilbert space

In this article one considers the measure, which is harmonic in a deleted neighbourhood. If this measure “grows” slower than the fundamental measure, then one proves that the singular point is removable.

Keywords:

• Measure
• Hilbert space
• Laplacian
• fundamental solution