Construction of a unique self-adjoint generator for a symmetric local semigroup |
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Authors: | Abel Klein Lawrence J Landau |
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Affiliation: | Department of Mathematics, University of California, Irvine, California 92717 U.S.A.;Mathematics Department, Bedford College, University of London, Regent''s Park, London NW1 4NS, England |
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Abstract: | A definition is given of a symmetric local semigroup of (unbounded) operators P(t) (0 ? t ? T for some T > 0) on a Hilbert space , such that P(t) is eventually densely defined as t → 0. It is shown that there exists a unique (unbounded below) self-adjoint operator H on such that P(t) is a restriction of e?tH. As an application it is proven that H0 + V is essentially self-adjoint, where e?tH0 is an Lp-contractive semigroup and V is multiplication by a real measurable function such that V ∈ L2 + ε and e?δV ∈ L1 for some ε, δ > 0. |
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