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Lower semicontinuhy of positive quadratic forms

  • Barry Simon (a1)

Synopsis

We develop various facets of the theory of quadratic forms on a Hilbert space suggested by a criterion of Kato which characterizes closed forms in terms of lower semicontinuity.

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References

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1Brezis, H.Maximal Monotone Operators (Amsterdam: North Holland, 1973).
2Dym, H. and McKean, H.Fourier Series and Integrals (London: Academic Press, 1972).
3Kato, T.Perturbation Theory for Linear Operators (Berlin: Springer, 1966).
4Lieb, E. H. and Simon, B.The Thomas-Fermi theory of Atoms, Molecules and Solids. Advances in Math. 23 (1977), 22116.
5Lieb, E. H. and simon, B.The Hartree-Fock Theory for Coulomb Systems. Comm. Math. Phys., 53 (1977), 185194.
6Reed, M. and Simon, B.Methods of Modern Mathematical Physics. I. Functional Analysis (London: Academic Press, 1972).
7Schechter, M. Cutoff Potentials and Forms Extensions. Yeshiva Univ. Preprint (1976).
8Simon, B. A Canonical Decomposition for Quadratic Forms with Applications Monotone Convergence Theorems. J. Functional Analysis, to appear.

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