Bivariational bounds on 〈ϕ,g〉, when Aϕ=f

  • M. F. Barnsley
  • P. D. Robinson
Contributed Lectures
Part of the Lecture Notes in Mathematics book series (LNM, volume 415)


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.


Hilbert Space Fourier Coefficient Variational Bound Boundary Term Linear Differential Equation 
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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • M. F. Barnsley
  • P. D. Robinson

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