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The essential self-adjointness of differential operators with positive coefficients

Published online by Cambridge University Press:  14 November 2011

R. G. Keller
R. G. Keller
Affiliation:
Mathematics Institute, University of Oxford
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Extract

We consider the formally self-adjoint 2mth-order elliptic differential operator in ℝn given by where lt is an operator of order t, and pt ≧0 for t ≧1 and establish conditions under which the operator on is essentially self-adjoint in L2. A feature is that the major conditions (including the positivity of the coefficients) have to be imposed only in an increasing sequence of annular regions surrounding the origin.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 3-4 , 1979 , pp. 345 - 360
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

1Eastham, M. S. P., Evans, W. D. and McLeod., J. B.The essential self-adjointness of Schrodingertype operators. Arch. Rational Mech. Anal. 60(1976), 184–204.Google Scholar
2Evans., W. D.On non-integrable square solutions of a fourth-order differential equation and the limit-2 classification. J. London Math. Soc. 7 (1973), 343–354.Google Scholar
3Everitt., W. N.Some positive definite differential operators. London Math. Soc. 43 (1968), 465–473.Google Scholar
4Kato., T.Schrodinger operators with singular potentials. Israel J. Math. 13 (1972), 135–148.Google Scholar
5Keller., R. G.The essential self-adjointness of differential operators. Proc. Roy. Soc. Edinb. Sect. A 82, (1979), 305–344.Google Scholar
6Schechter., M.Spectra of Partial Differential Operators (Amsterdam: North-Holland, 1971).Google Scholar