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On the spectral function of some higher order elliptic or degenerate-elliptic operators

Abstract : We study the spectral function lambda --> s(lambda) := s(-A+lambda V) where s(-A+lambda V) denotes the spectral bound of the perturbed operator -A+lambda V and V is a suitable potential. In the case where A = (-1)(m) (\alpha\=\beta\=m)Sigma D-alpha(a(alpha beta)D(beta)) is a higher order degenerate-elliptic operator on L-2(R-N) and V is an element of L-1(R-N) we show in particular that s(lambda) > 0 for all lambda > 0 provided that integral(RN) V(x)dx greater than or equal to 0, V not equal 0 and N less than or equal to 2m.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00694257
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Submitted on : Thursday, May 3, 2012 - 11:34:21 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

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Em Ouhabaz. On the spectral function of some higher order elliptic or degenerate-elliptic operators. Semigroup Forum, Springer Verlag, 1998, 57 (3), pp.305--314. ⟨10.1007/PL00005980⟩. ⟨hal-00694257⟩

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