Abstract
For a certain q-difference operator introduced and studied in a series of articles by the same authors, we investigate its extreme self-adjoint extensions, i.e., the so-called Friedrichs and Kreǐn extensions. We show that for the interval of parameters under consideration, the Friedrichs extension and the Kreǐn extension are distinct and give values of the parameter in the von Neumann formulas that correspond to those extensions and describe their resolvent operators. A crucial role in our investigation plays the fact that both the Friedrichs and the Kreǐn extensions are scale invariant. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Recommended Citation
M. B. Bekker et al., "Extreme Self-adjoint Extensions of a Semibounded Q-difference Operator," Mathematische Nachrichten, vol. 287, no. 8 thru 9, pp. 869 - 884, Wiley; Wiley-VCH Verlag, Jun 2014.
The definitive version is available at https://doi.org/10.1002/mana.201200261
Department(s)
Mathematics and Statistics
Publication Status
Full Access
Keywords and Phrases
Friedrichs extension; Kreǐn extension; q-difference operator; Scale-invariant; Self-adjoint
International Standard Serial Number (ISSN)
1522-2616; 0025-584X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Wiley; Wiley-VCH Verlag, All rights reserved.
Publication Date
01 Jun 2014
