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

By Andrea Posilicano. 2003

61 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0bb80e1011a3c337423d832a38422420acbc2db2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains (2009, unknown): “13], [76], [79], [80], [81], [82], [83], [84], [87], [88], [89], [95], [100], [101], [102], [103], [104], [105], [106], [107], [108], [111], [112], [113], [114], [119], [120], [121], [127], and the references cited therein.”
SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS (2006, background): “[124] for the discussion of elliptic boundary conditio ns. In some cases there are natural boundary triples reflecting some specific proper ties of the problem, like in the theory of singular perturbations, see [ 114 ] and s ubsection 1.4.2 below.”
Boundary pairs associated with quadratic forms (2012, background): “Posilicano’s approach Posilicano [74] (see also [73], [72]) considers (in our notation) a self-adjoint extension H D and a bounded operator ′ : dom H D → G (dom H D with its graph norm) which is surjective and has dense kernel.”
Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples (2012, background): “Many papers have been written on Krein’s formula; see, e.g. [Derkach and Malamud, 1991; Gesztesy, Makarov and Tsekanovskii, 1998; Krĕın, 1946; Langer and Textorius, 1977; Pankrashkin, 2006; Saakjan, 1965] for the general case and, e.g. [Gesztesy and Mitrea, 2008, 2009, 2011; Grubb, 2008; Posilicano”
Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “General operator models for highly singular perturbations involve lifting of operators in Pontryagin spaces [117, 239, 240, 241, 252, 256, 640, 641, 707].”
Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr\ (2008, unknown): “13], [54], [55], [59], [64], [65], [68]–[71], [79].”
Self-adjoint Extensions of Restrictions (2007, unknown): “ar X iv :m at h- ph /0 70 30 78 v3 2 8 M ar 2 00”
Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\ (2008, unknown): “3], [61], [62], [66], [74], [75], [78], [79], [82], [83], [94].”