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- W47460812 abstract "We study the Schrodinger operator $L=-Delta+V$ on a star-shaped domain $Omega$ in $mathbb{R}^d$ with Lipschitz boundary $partialOmega$. The operator is equipped with quite general Dirichlet- or Robin-type boundary conditions induced by operators between $H^{1/2}(partialOmega)$ and $H^{-1/2}(partialOmega)$, and the potential takes values in the set of symmetric $Ntimes N$ matrices. By shrinking the domain and rescaling the operator we obtain a path in the Fredholm-Lagrangian-Grassmannian of the subspace of $H^{1/2}(partialOmega)times H^{-1/2}(partialOmega)$ corresponding to the given boundary condition. The path is formed by computing the Dirichlet and Neumann traces of weak solutions to the rescaled eigenvalue equation. We prove a formula relating the number of negative eigenvalues of $L$ (the Morse index), the signed crossings of the path (the Maslov index), the number of negative eigenvalues of the potential matrix evaluated at the center of the domain, and the number of negative squares of a bilinear form related to the boundary operator." @default.
- W47460812 created "2016-06-24" @default.
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- W47460812 date "2014-08-05" @default.
- W47460812 modified "2023-09-27" @default.
- W47460812 title "The Morse and Maslov indices for multidimensional Schrodinger operators with matrix-valued potentials" @default.
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