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Weighted Laplace Spaces for Spectral Measures and Rational Approximation
We introduce the weighted Laplace space $H_w$, an RKHS of Laplace transforms on $(0,\infty)$, and study spectral measures in its dual space $H'_w$. For conforming FEM discretizations of the Dirichlet Laplacian on bounded Lipschitz domains, we prove the dual-norm inequality $\|μ_h\|_{H'_w} \leq \|μ\|
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