Trotter?s product formula for projections

• DOI: 10.1007/s00013-003-0537-2
• Publication Date: 2004-03-29T14:37:32Z
• Authors: M. Matolcsi; R. Shvidkoy
• Keywords: QA Mathematics / matematika; 0101 mathematics; 01 natural sciences

The aim of this paper is to examine the convergence of Trotter’s product formula when one of the C 0-semigroups is replaced by a projection (which can always be regarded as a constant degenerate semigroup). The motivaton to study Trotter’s formula in this setting arises from the fact that for ‘nice’ open sets $\Omega \subset \mathbb{R}^n$ the C 0-semigroup on $L^{2}(\Omega)$ generated by the Laplacian with Dirichlet boundary conditions can be obtained as a limit of a formula of this type.