A simplicity criterion for symmetric operator on a graph

Abstract

In the present paper we show that the topology of the underlying graph determines the domain and deficiency indices of a certain associated minimal symmetric operator. We obtaine a criterion of simplicity for the minimal operator associated with the graph.

Key words: Laplace operator, quantum graph, symmetric operator, deficiency indices.

Full Text

Article Information

Title	A simplicity criterion for symmetric operator on a graph
Source	Methods Funct. Anal. Topology, Vol. 20 (2014), no. 2, 117-123
MathSciNet	MR3242860
zbMATH	1313.47093
Milestones	Received 28/10/2013; Revised 12/11/2013
Copyright	The Author(s) 2014 (CC BY-SA)

Authors Information

E. N. Ashurova
Tavrida National V. I. Vernadsky University, 4 Academician Vernadsky Ave., Simferopol, 95007, Ukraine

A. N. Kandagura
Tavrida National V. I. Vernadsky University, 4 Academician Vernadsky Ave., Simferopol, 95007, Ukraine

I. I. Karpenko
Tavrida National V. I. Vernadsky University, 4 Academician Vernadsky Ave., Simferopol, 95007, Ukraine 

Citation Example

E. N. Ashurova, A. N. Kandagura, and I. I. Karpenko, A simplicity criterion for symmetric operator on a graph, Methods Funct. Anal. Topology 20 (2014), no. 2, 117-123.

BibTex

@article {MFAT720,
    AUTHOR = {Ashurova, E. N. and Kandagura, A. N. and Karpenko, I. I.},
     TITLE = {A simplicity criterion for symmetric operator on a graph},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {20},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {117-123},
      ISSN = {1029-3531},
  MRNUMBER = {MR3242860},
 ZBLNUMBER = {1313.47093},
       URL = {http://mfat.imath.kiev.ua/article/?id=720},
}