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Mat. Zametki, 2004, Volume 76, Issue 6, Pages 905–917 (Mi mz162)  

This article is cited in 6 scientific papers (total in 6 papers)

On a Result of R. Turner

N. B. Uskova

Voronezh State Technical University

Abstract: We study the similarity of perturbed compact operators to operators of block-diagonal structure with respect to some family of orthogonal projection operators, which allows us to refine and essentially strengthen results due to R.  Turner. We obtain information about the operator realizing the similarity transformation, present estimates for the eigenvalues and eigenvectors of the perturbed operator, and also study the inverse problem of spectral analysis.

DOI: https://doi.org/10.4213/mzm162

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English version:
Mathematical Notes, 2004, 76:6, 844–854

Bibliographic databases:

UDC: 517.9
Received: 03.04.2002

Citation: N. B. Uskova, “On a Result of R. Turner”, Mat. Zametki, 76:6 (2004), 905–917; Math. Notes, 76:6 (2004), 844–854

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Uskova N.B., “On the spectral properties of a second-order differential operator with a matrix potential”, Differ. Equ., 52:5 (2016), 557–567  crossref  mathscinet  zmath  isi  elib  scopus
    2. G. V. Garkavenko, N. B. Uskova, “Metod podobnykh operatorov v issledovanii spektralnykh svoistv raznostnykh operatorov s rastuschim potentsialom”, Sib. elektron. matem. izv., 14 (2017), 673–689  mathnet  crossref
    3. N. B. Uskova, G. V. Garkavenko, “Teorema o rasscheplenii lineinykh operatorov i asimptotika sobstvennykh znachenii raznostnykh operatorov s rastuschim potentsialom”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 91–106  mathnet  crossref
    4. Baskakov A.G. Krishtal I.A. Uskova N.B., “Linear Differential Operator With An Involution as a Generator of An Operator Group”, Oper. Matrices, 12:3 (2018), 723–756  crossref  mathscinet  zmath  isi
    5. N. B. Uskova, “Matrichnyi analiz spektralnykh proektorov vozmuschennykh samosopryazhennykh operatorov”, Sib. elektron. matem. izv., 16 (2019), 369–405  mathnet  crossref
    6. Baskakov A.G., Krishtal I.A., Uskova N.B., “Similarity Techniques in the Spectral Analysis of Perturbed Operator Matrices”, J. Math. Anal. Appl., 477:2 (2019), 930–960  crossref  isi
  • Математические заметки Mathematical Notes
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