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# 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.

### 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},
}