Spectral functions of the simplest even order ordinary differential operator

Abstract

We consider the minimal differential operator $A$ generated in $L^2(0,\infty)$ by the differential expression $l(y) = (-1)^n y^{(2n)}$. Using the technique of boundary triplets and the corresponding Weyl functions, we find explicit form of the characteristic matrix and the corresponding spectral function for the Friedrichs and Krein extensions of the operator $A$.

Key words: Friedrichs and Krein extensions, spectral function, boundary triplet, Weyl function, Vandermonde determinant.

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Article Information

Title	Spectral functions of the simplest even order ordinary differential operator
Source	Methods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 319-326
MathSciNet	MR3156298
zbMATH	1313.47095
Milestones	Received 02/07/2013
Copyright	The Author(s) 2013 (CC BY-SA)

Authors Information

Anton Lunyov
R. Luxemburg, 74, Donetsk, 83114, Ukraine 02/07/2013

Citation Example

Anton Lunyov, Spectral functions of the simplest even order ordinary differential operator, Methods Funct. Anal. Topology 19 (2013), no. 4, 319-326.

BibTex

@article {MFAT701,
    AUTHOR = {Lunyov, Anton},
     TITLE = {Spectral functions of the simplest even order ordinary differential operator},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {319-326},
      ISSN = {1029-3531},
  MRNUMBER = {MR3156298},
 ZBLNUMBER = {1313.47095},
       URL = {http://mfat.imath.kiev.ua/article/?id=701},
}