Extreme self-adjoint extensions of a semibounded q-difference operator

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 Kreĭn extensions. We show that for the interval of parameters under consideration, the Friedrichs extension a...

Full description

Saved in:
Bibliographic Details
Published inMathematische Nachrichten Vol. 287; no. 8-9; pp. 869 - 884
Main Authors B. Bekker, Miron, J. Bohner, Martin, Voulov, Hristo
Format Journal Article
LanguageEnglish
Published Weinheim Blackwell Publishing Ltd 01.06.2014
Wiley Subscription Services, Inc
Subjects
34N05
39A12
39A13
47B25
47B37
47B39
Friedrichs extension
Kreĭn extension
q-difference operator
scale-invariant
self-adjoint
Online AccessGet full text

Cover

More Information
Summary: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 Kreĭn extensions. We show that for the interval of parameters under consideration, the Friedrichs extension and the Kreĭn 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 rôle in our investigation plays the fact that both the Friedrichs and the Kreĭn extensions are scale invariant.
Bibliography:istex:F628A8FD5C01B27992E40673F05C2359F80B2548
ark:/67375/WNG-0D1SHZKM-5
ArticleID:MANA201200261
University of Pittsburgh at Johnstown
College Research Council
e‐mail
voulovh@umkc.edu
bekker@pitt.edu
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201200261