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A variational problem in Hilbert space

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Abstract

Letℋ be a Hilbert space over the field of complex numbers, with inner product (g,h). Letf be a fixed element inℋ, and letH be a compact, self-adjoint linear operator onℋ. We find the maximum value ofQ f (u)=|(f,u)|2 in the classU of elementsu inℋ for which (u,u)=1, (u, Hu)=0.

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References

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  3. G. Helmberg,Introduction to Spectral Theory in Hilbert Space, North Holland Publishing Company (1969), Amsterdam.

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Authors and Affiliations

  1. Howard University, Washington, D.C., USA

    J. Ernest Wilkins Jr.

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  1. J. Ernest Wilkins Jr.
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Wilkins, J.E. A variational problem in Hilbert space. Appl Math Optim 2, 265–270 (1975). https://doi.org/10.1007/BF01464272

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  • DOI: https://doi.org/10.1007/BF01464272

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