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Mat. Zametki, 2008, Volume 83, Issue 1, Pages 39–49 (Mi mz3764)  

This article is cited in 4 scientific papers (total in 4 papers)

Regularized Traces of Higher-Order Singular Differential Operators

A. I. Kozko, A. S. Pechentsov

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

Abstract: We consider singular differential operators of order $2m$, $m\in\mathbb N$, with discrete spectrum in $L_2[0,+\infty)$. For self-adjoint extensions given by the boundary conditions $y(0)=y"(0)=\dotsb=y^{(2m-2)}(0)=0$ or $y'(0)=y"'(0)=\dotsb=y^{(2m-1)}(0)=0$, we obtain regularized traces. We present the explicit form of the spectral function, which can be used for calculating regularized traces.

Keywords: singular differential operator, regularized trace, Hilbert space, spectral function, Sturm–Liouville problem, self-adjoint extension, Green function

DOI: https://doi.org/10.4213/mzm3764

Full text: PDF file (485 kB)
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English version:
Mathematical Notes, 2008, 83:1, 37

Bibliographic databases:

UDC: 517.94
Received: 30.03.2006

Citation: A. I. Kozko, A. S. Pechentsov, “Regularized Traces of Higher-Order Singular Differential Operators”, Mat. Zametki, 83:1 (2008), 39–49; Math. Notes, 83:1 (2008), 37

Citation in format AMSBIB
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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. A. I. Kozko, A. S. Pechentsov, “The spectral function of a singular differential operator of order $2m$”, Izv. Math., 74:6 (2010), 1205–1224  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  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  scopus
    3. Nazarov A.I., Stolyarov D.M., Zatitskiy P.B., “The Tamarkin Equiconvergence Theorem and a First-Order Trace Formula For Regular Differential Operators Revisited”, J. Spectr. Theory, 4:2 (2014), 365–389  crossref  mathscinet  zmath  isi  scopus
    4. A. I. Kozko, “O nekotorykh priznakakh skhodimosti dlya znakopostoyannykh i znakochereduyuschikhsya ryadov”, Chebyshevskii sb., 18:1 (2017), 123–133  mathnet  crossref  elib
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