Abstract
If v1 and V2 are two best L1-approximants to f ∈ L1(X) from a vector subspace V ⊂ L1(X), then (f-v1) (f-V2) ≥ 0 a.e. on X, where (X, A, μ) is a given measure space. This simple inequality helps to derive the uniqueness of a best harmonic L1-approximant to a given subharmonic function under weak assumptions. In addition, an existence theorem for best harmionic L1-approximants is given.
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© 1987 Birkhäuser Verlag Basel
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Haussmann, W., Rogge, L. (1987). Uniqueness Inequality and Best Harmonic L1-Approximation. In: Walter, W. (eds) General Inequalities 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7192-1_12
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DOI: https://doi.org/10.1007/978-3-0348-7192-1_12
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