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31.—Spectral Manifolds for Constant Coefficient Elliptic Operators in Lp(Rn)*

Published online by Cambridge University Press:  14 February 2012

M. Thompson
M. Thompson
Affiliation:
Mathematics Division, University of Sussex.
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Synopsis

The principal results of this paper concern the spectral properties of the maximal realisation Pp in Lp(Rn) of a formally self adjoint constant coefficient strongly elliptic partial differential operator P(D), assumed to be homogeneous of order 2m, for 1 ≦ p ≦ ∞ and n ≧ 2. If we assume that , for 2n/n + l ≦ p ≦ 2n/n−1, together with certain assumptions on the associated real zero surfaces P(ξ) = λ, λ > 0, then σ(Pp) = σc(Pp) = [0, ∞). We obtain an estimate on the norm of the resolvent of Pp for points near the real axis, which allows us to establish the existence of a generalised resolution of the identity in the sense of Kocan.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 4 , 1975 , pp. 359 - 369
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

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