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We study a family of differential operators Lα in two variables, depending on the coupling parameter α?0 that appears only in the boundary conditions. Our main concern is the spectral properties of Lα, which turn out to be quite different for α<1 and for α>1. In particular, Lα has a unique self-adjoint realization for α<1 and many such realizations for α>1. In the more difficult case α>1 an analysis of non-elliptic pseudodifferential operators in dimension one is involved. 相似文献
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Crossing by lines all edges of a line arrangement 总被引:1,自引:0,他引:1
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In this article, we construct simply connected symplectic Calabi–Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T4. Using our method, we also construct symplectic non-Kähler Calabi–Yau 6-manifolds with fundamental group Z. This paper also produces the first examples of simply connected and non-simply connected symplectic Calabi–Yau 6-manifolds with fundamental groups Zp×Zq, and Z×Zq for any p≥1 and q≥2via co-isotropic Luttinger surgery. 相似文献