Boundary triples and Weyl functions for singular perturbations of self-adjoint operators

Given the symmetric operator $A_N$ obtained by restricting the self-adjoint operator $A$ to $N$, a linear dense set, closed with respect to the graph norm, we determine a convenient boundary triple for the adjoint $A_N^*$ and the corresponding Weyl function. These objects provide us with the self-adjoint extensions of $A_N$ and their resolvents.

[1]  H. Neidhardt,et al.  Weyl function and spectral properties of self-adjoint extensions , 2002 .

[2]  A. Posilicano Self-adjoint extensions by additive perturbations , 2001, math/0104226.

[3]  A. Posilicano Boundary Conditions for Singular Perturbations of Self-adjoint Operators , 2001, math/0102018.

[4]  A. Posilicano A Krein-like Formula for Singular Perturbations of Self-Adjoint Operators and Applications , 2000, math/0005082.

[5]  F. Gesztesy,et al.  An Addendum to Krein's Formula , 1997, funct-an/9711003.

[6]  P. Seba,et al.  Schrödinger-Operators with Singular Interactions , 1994 .

[7]  V. Gorbachuk,et al.  Boundary Value Problems for Operator Differential Equations , 1990 .

[8]  V. Bruk On a Class of Boundary Value Problems with Spectral Parameter in the Boundary Condition , 1976 .

[9]  J. Neumann,et al.  Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren , 1930 .

[10]  P. Exner,et al.  Curvature-Induced Bound States for a δ Interaction Supported by a Curve in R 3 , 2002 .

[11]  V. Koshmanenko Singular Operator as a Parameter of Self-adjoint Extensions , 2000 .

[12]  K. Makarov Tsekanovskii: An Addendum to Krein’s Formula , 1998 .

[13]  V. Derkach,et al.  The extension theory of Hermitian operators and the moment problem , 1995 .

[14]  S. Albeverio,et al.  Square Powers of Singularly Perturbed Operators , 1995 .

[15]  V. Derkach,et al.  Generalized resolvents and the boundary value problems for Hermitian operators with gaps , 1991 .

[16]  Anatoly N. Kochubei,et al.  Extensions of symmetric operators and symmetric binary relations , 1975 .