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On the Krein and Friedrichs extensions of a positive Jacobi operator

Brown, B. Malcolm and Christiansen, Jacob S. LU (2005) In Expositiones Mathematicae 23(2). p.179-186
Abstract

We show that for a positive linear operator acting in ℓ2 and defined from anxn+1 + bn xn + an-1xn-1 its so-called Friedrichs and Krein extensions may be explicitly characterized by boundary conditions as n → ∞.

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author
and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Boundary conditions, Difference equations, Minimal solution, Positive self-adjoint extensions, Unbounded Jacobi operators
in
Expositiones Mathematicae
volume
23
issue
2
pages
8 pages
publisher
Elsevier
external identifiers
  • scopus:20844450747
ISSN
0723-0869
DOI
10.1016/j.exmath.2005.01.020
language
English
LU publication?
no
id
b87b7cf0-893d-4999-b99f-c1c6828a0c35
date added to LUP
2025-07-11 11:45:25
date last changed
2025-10-14 11:13:58
@article{b87b7cf0-893d-4999-b99f-c1c6828a0c35,
  abstract     = {{<p>We show that for a positive linear operator acting in ℓ<sup>2</sup> and defined from a<sub>n</sub>x<sub>n+1</sub> + b<sub>n</sub> x<sub>n</sub> + a<sub>n-1</sub>x<sub>n-1</sub> its so-called Friedrichs and Krein extensions may be explicitly characterized by boundary conditions as n → ∞.</p>}},
  author       = {{Brown, B. Malcolm and Christiansen, Jacob S.}},
  issn         = {{0723-0869}},
  keywords     = {{Boundary conditions; Difference equations; Minimal solution; Positive self-adjoint extensions; Unbounded Jacobi operators}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{179--186}},
  publisher    = {{Elsevier}},
  series       = {{Expositiones Mathematicae}},
  title        = {{On the Krein and Friedrichs extensions of a positive Jacobi operator}},
  url          = {{http://dx.doi.org/10.1016/j.exmath.2005.01.020}},
  doi          = {{10.1016/j.exmath.2005.01.020}},
  volume       = {{23}},
  year         = {{2005}},
}