Geodesic
Perturbation of differential operators on high-codimension manifold and the extension theory for symmetric linear relations in an indefinite metric space
Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 3, pp. 466-472

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The problem of realization of nontrivial perturbations supported on thin sets of “codimension” $\nu$ in $R^n$ for elliptic operators of order $m$, when $\nu\geqslant 2m$, is formulated as one of construction of the self-adjoint extensions of some symmetric linear relation in an indefinite metric space. The self-adjoint extensions and their resolvents are described. It is found that the same extensions can be obtained as a result of extensions of some symmetric operator in $L_2(R^n)$ with outgoing to a larger indefinite metric space. But such operator is picked out already by the “nonlocal” boundary conditions. Applications to quantum models of point interactions are discussed. 
@article{TMF_1992_92_3_a8,
     author = {Yu. G. Shondin},
     title = {Perturbation of differential operators on high-codimension manifold and the extension theory for symmetric linear relations in an indefinite metric space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {466--472},
     publisher = {mathdoc},
     volume = {92},
     number = {3},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_92_3_a8/}
}
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Yu. G. Shondin. Perturbation of differential operators on high-codimension manifold and the extension theory for symmetric linear relations in an indefinite metric space. Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 3, pp. 466-472. http://geodesic.mathdoc.fr/item/TMF_1992_92_3_a8/