Trotter?s product formula for projections

QA Mathematics / matematika 0101 mathematics 01 natural sciences
DOI: 10.1007/s00013-003-0537-2 Publication Date: 2004-03-29T14:37:32Z
ABSTRACT
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.
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