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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 6, Pages 107–126 (Mi izv2780)  

This article is cited in 3 scientific papers (total in 3 papers)

The spectral function of a singular differential operator of order $2m$

A. I. Kozko, A. S. Pechentsov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study the spectral function of a self-adjoint semibounded below differential operator on a Hilbert space $L_2[0,\infty)$ and obtain the formulae for the spectral function of the operator $(-1)^{m}y^{(2m)}(x)$ with general boundary conditions at the zero. In particular, for the boundary conditions $y(0)=y'(0)=…=y^{(m-1)}(0)=0$ we find the explicit form of the spectral function $\Theta_{mB'}(x,x,\lambda)$ on the diagonal $x=y$ for $\lambda \ge 0$.

Keywords: spectral function, eigenvalues, self-adjoint differential operator, regularized traces, singular differential operators, Green's function.

DOI: https://doi.org/10.4213/im2780

Full text: PDF file (583 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:6, 1205–1224

Bibliographic databases:

Document Type: Article
UDC: 517.94
MSC: Primary 47E05; Secondary 34B05, 34L15, 34L20, 47B25, 58C10
Received: 07.03.2008
Revised: 31.10.2009

Citation: A. I. Kozko, A. S. Pechentsov, “The spectral function of a singular differential operator of order $2m$”, Izv. RAN. Ser. Mat., 74:6 (2010), 107–126; Izv. Math., 74:6 (2010), 1205–1224

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kozko A.I., Pechentsov A.S., “Regulyarizovannye sledy singulyarnykh differentsialnykh operatorov s kanonicheskimi kraevymi usloviyami”, Vestn. Mosk. un-ta. Ser. 1. Matem. Mekh., 2011, no. 4, 11–17  mathscinet  zmath  elib
    2. Zatitskiy P.B., Nazarov A.I., Stolyarov D.M., “Formula of regularized traces”, Dokl. Math., 85:1 (2012), 29–32  crossref  mathscinet  zmath  isi  elib  elib
    3. A. I. Kozko, “O nekotorykh priznakakh skhodimosti dlya znakopostoyannykh i znakochereduyuschikhsya ryadov”, Chebyshevskii sb., 18:1 (2017), 123–133  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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