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Ufa Mathematical Journal, 2017, Volume 9, Issue 4, Pages 85–96
DOI: https://doi.org/10.13108/2017-9-4-85
(Mi ufa408)
 

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

Spectral decomposition of normal operator in real Hilbert space

M. N. Oreshina

Lipetsk State Technical University, Moskovskaya str. 30, 398600, Lipetsk, Russia
References:
Abstract: We consider normal unbounded operators acting in a real Hilbert space. The standard approach to solving spectral problems related with such operators is to apply the complexification, which is a passage to a complex space. At that, usually, the final results are to be decomplexified, that is, the reverse passage is needed. However, the decomplexification often turns out to be nontrivial.
The aim of the present paper is to extend the classical results of the spectral theory for the case of normal operators acting in a real Hilbert space. We provide two real versions of the spectral theorem for such operators.
We construct the functional calculus generated by the real spectral decomposition of a normal operator. We provide examples of using the obtained functional calculus for representing the exponent of a normal operator.
Keywords: unbounded normal operator, real Hilbert space, complexification, spectral theorem, functional calculus.
Received: 22.05.2016
Bibliographic databases:
Document Type: Article
UDC: 517.984
MSC: 47B15
Language: English
Original paper language: Russian
Citation: M. N. Oreshina, “Spectral decomposition of normal operator in real Hilbert space”, Ufa Math. J., 9:4 (2017), 85–96
Citation in format AMSBIB
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\by M.~N.~Oreshina
\paper Spectral decomposition of normal operator in real Hilbert space
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 4
\pages 85--96
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\elib{https://elibrary.ru/item.asp?id=30562595}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85038119218}
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  • https://doi.org/10.13108/2017-9-4-85
  • https://www.mathnet.ru/eng/ufa/v9/i4/p87
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
    Statistics & downloads:
    Abstract page:417
    Russian version PDF:395
    English version PDF:99
    References:53
     
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