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The spaces H s (∂Ω) are described via Steklov eigenfunction expansions. This characterization provides explicit formulae for the inner products, norms and allows the description of explicit orthonormal bases for these spaces. It uses a special inner product on H 1 (Ω), and properties of the harmonic Steklov eigenfunctions on the region. This approach only requires the boundary of the region be Lipschitz and generalizes the classical definitions that are used when the boundary is a smooth manifold.

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