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Trotter’s product formula for projections. (English) Zbl 1054.47033

Author’s 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.”

MSC:

47D06 One-parameter semigroups and linear evolution equations
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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