We give necessary and sufficient conditions for the lower bound (Pu, u) ≥ - C K ∥ u ∥ 2(1/2), C K > 0, ∀ u ∈ C∞0 (K) to hold for any compact set K ⊂ X, an open set of ℝn, for certain pseudodifferential operators P = P* ∈ Ψ4phg(X) with p(x, ξ) ∼ ∑mi=1 (qi2)2 + p3 + p2 + ⋯, ∑i qi2 being transversally elliptic with respect to the characteristic manifold ∑ = ∩i(qi2)-1 (0).
Parmeggiani, A. (1998). Necessary and sufficient conditions for the almost-positivity of certain 4th-order pseudodifferential operators. A generalization. FORUM MATHEMATICUM, 10(3), 277-301 [10.1515/form.10.3.277].
Necessary and sufficient conditions for the almost-positivity of certain 4th-order pseudodifferential operators. A generalization
Parmeggiani A.
1998
Abstract
We give necessary and sufficient conditions for the lower bound (Pu, u) ≥ - C K ∥ u ∥ 2(1/2), C K > 0, ∀ u ∈ C∞0 (K) to hold for any compact set K ⊂ X, an open set of ℝn, for certain pseudodifferential operators P = P* ∈ Ψ4phg(X) with p(x, ξ) ∼ ∑mi=1 (qi2)2 + p3 + p2 + ⋯, ∑i qi2 being transversally elliptic with respect to the characteristic manifold ∑ = ∩i(qi2)-1 (0).File in questo prodotto:
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