Abstract
We give a precise sense to the notion of singular perturbation. It is a bilinear form b in a Hilbert space H with a regular (closable) component br = o. Further we propose a classification of singular bilinear forms with respect to a fixed selfadjoint operator A ⩾ o in H. Finally we present a construction of the singularly perturbed operator Ab. Our definition of Ab is based on the interpretation of b as a boundary condition for a fixed selfadjoint extension of the symmetric operator A0 = Ao = A↾Ker b.
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© 1989 Springer-Verlag
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Koshmaneuko, V.D. (1989). Singular perturbations defined by forms. In: Exner, P., Šeba, P. (eds) Applications of Self-Adjoint Extensions in Quantum Physics. Lecture Notes in Physics, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022958
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DOI: https://doi.org/10.1007/BFb0022958
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