Abstract
The spectral aspect of the problem of perturbations supported on thin sets of codimension θ≥2m in ℝn is considered for elliptic operators of order m. The problem of realization of such perturbations is formulated as a problem of self-adjoint extension of a linear symmetric relation in a space with indefinite metric. It is shown how to construct such a relation for a given elliptic operator and a family of distributions. Its functional model is obtained in terms of Q-functions. Self-adjoint extensions and their resolvents are described. The theory developed is applied to quantum models of point interactions in high dimensions and high moments. Bibliography: 35 titles.
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