Bivariational bounds on 〈ϕ,g〉, when Aϕ=f
Complementary (upper and lower) bivariational bounds are presented on the inner product 〈φ,g〉 associated with the linear equation Aφ=f in a Hilbert space, where the operator A is self-adjoint. The vector g is arbitrary. Possible applications are mentioned, including the derivation of point-wise bounds on φ. Variational bounds on 〈φ,f〉 are taken as a starting-point.
KeywordsHilbert Space Fourier Coefficient Variational Bound Boundary Term Linear Differential Equation
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