Boundary Conditions for Singular Perturbations of Self-Adjoint Operators

@inproceedings{Posilicano2001BoundaryCF,
  title={Boundary Conditions for Singular Perturbations of Self-Adjoint Operators},
  author={Andrea Posilicano},
  year={2001}
}
Let A : D(A) ⊆ H → H be an injective self-adjoint operator and let τ : D(A) → X, X a Banach space, be a surjective linear map such that ‖τφ‖X ≤ c ‖Aφ‖H. Supposing that Kernel τ is dense in H, we define a family AτΘ of self-adjoint operators which are extensions of the symmetric operator A|{τ=0} . Any φ in the operator domain D(A τ Θ) is characterized by a sort of boundary conditions on its univocally defined regular component φreg, which belongs to the completion of D(A) w.r.t. the norm ‖Aφ‖H… CONTINUE READING

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