Complete nonselfadjointness for Schrödinger operators on the semi-axis-Reference-Cited by-同舟云学术

Complete nonselfadjointness for Schrödinger operators on the semi-axis

Published:2024-04-12 Issue:1 Volume:35 Page:217-232
ISSN:1061-0022
Container-title:St. Petersburg Mathematical Journal
language:en
Short-container-title:St. Petersburg Math. J.

Author:

Fischbacher C.,Naboko S.,Wood I.

Abstract

This note is devoted to the study of complete nonselfadjointness for all maximally dissipative extensions of a Schrödinger operator on a half-line with dissipative bounded potential and dissipative boundary condition. It is shown that all maximally dissipative extensions that preserve the differential expression are completely nonselfadjoint. However, it is possible for maximally dissipative extensions to have a one-dimensional reducing subspace on which the operator is selfadjoint. A characterization of these extensions and the corresponding subspaces is given, accompanied by a specific example.

Publisher

American Mathematical Society (AMS)

Reference25 articles.

1. On the theory of dilatation and on the spectral analysis of dissipative Schrödinger operators in the case of the Weyl limit circle;Allakhverdiev, B. P.;Izv. Akad. Nauk SSSR Ser. Mat.,1990

2. Boundary triplets and maximal accretive extensions of sectorial operators;Arlinskiĭ, Yury,2012

3. The functional model for maximal dissipative operators (translation form): an approach in the spirit of operator knots;Brown, Malcolm;Trans. Amer. Math. Soc.,2020

4. \bysame, The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach, Algebra i Analiz 35 (2023), no. 1, 33–79.

5. On the extension problem for dissipative operators;Crandall, Michael G.;J. Functional Analysis,1968