On the extremal extensions of a non-negative Jacobi operator

Abstract

We consider the minimal non-negative Jacobi operator with $p\times p-$matrix entries. Using the technique of boundary triplets and the corresponding Weyl functions, we describe the Friedrichs and Krein extensions of the minimal Jacobi operator. Moreover, we parametrize the set of all non-negative extensions in terms of boundary conditions.

Key words: Jacobi matrix, non-negative operator, Friedrichs and Krein extensions, boundary triplet, Weyl function.

Full Text

Article Information

Title	On the extremal extensions of a non-negative Jacobi operator
Source	Methods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 310-318
MathSciNet	MR3156297
zbMATH	1313.47065
Milestones	Received 02/04/2013; Revised 14/06/2013
Copyright	The Author(s) 2013 (CC BY-SA)

Authors Information

Aleksandra Ananieva
R. Luxemburg, 74, Donetsk, 83114, Ukraine

Nataly Goloshchapova
R. Luxemburg, 74, Donetsk, 83114, Ukraine 

Citation Example

Aleksandra Ananieva and Nataly Goloshchapova, On the extremal extensions of a non-negative Jacobi operator, Methods Funct. Anal. Topology 19 (2013), no. 4, 310-318.

BibTex

@article {MFAT690,
    AUTHOR = {Ananieva, Aleksandra and Goloshchapova, Nataly},
     TITLE = {On the extremal extensions of a non-negative Jacobi operator},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {310-318},
      ISSN = {1029-3531},
  MRNUMBER = {MR3156297},
 ZBLNUMBER = {1313.47065},
       URL = {http://mfat.imath.kiev.ua/article/?id=690},
}