SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS

By J. Bruening, V. Geyler, Konstantin Pankrashkin. 2006

216 citations recorded by the source corpus.

We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of self-adjoint extensions in terms of the corresponding Krein maps (Weyl functions) is given. Applications include quantum graphs, point interactions, hybrid spaces and singular perturbations.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/752593b0820a33e30c28c13da449cbdb13207a53

How researchers see this paper

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

In Applied Mathematics

1. Jussi Behrndt
2. Fritz Gesztesy
3. M. Mitrea
4. H. D. de Snoo
5. S. Hassi
6. Ian Wood
7. B. M. Brown
8. Gerd Grubb

In Mathematical Physics

1. Jussi Behrndt
2. Fritz Gesztesy
3. M. Mitrea
4. H. D. de Snoo
5. S. Hassi
6. Olaf Post
7. Ian Wood
8. B. M. Brown

In Statistical and Nonlinear Physics

1. S. Hassi
2. Jussi Behrndt
3. Fritz Gesztesy
4. Andrea Posilicano
5. H. D. de Snoo

Citations in the corpus

• M ‐functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems (2008, background): “Further recent developments in this area can be found in [3, 8, 12, 38].”
• Self-adjoint Extensions of Restrictions (2007, methodology): “In Section 4 we explore, by using the results in [28], the connection with Boundary Triples theory of self-adjoint extensions (see e.g. [4], [16], [12], [10], [ 5 ]).”
• A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains (2009, background): “84], [6], [7], [9], [10], [16], [17], [23], [24], [25], [26], [29], [30], [32], [33], [34], [35], [36], [38], [39], [40], [41], [51], [52], [53], [58], [59], [60, Ch.”
• Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “5, which can be found in a different form in [184].”
• Square‐integrable solutions and Weyl functions for singular canonical systems (2011, background): “Furthermore, the reader is referred to [5]–[7], [9], [10], [12], [20], [21], [30], [53], [55] for some recent extensions and applications of the concept of boundary triplets and their Weyl functions.”
• Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr\ (2008, unknown): “84], [3], [7], [8], [11], [13], [14], [18], [20], [21], [33], [34], [39, Ch.”