RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i Analiz, 2018, Volume 30, Issue 3, Pages 93–111 (Mi aa1597)  

Research Papers

A functional model for the Fourier–Plancherel operator truncated to the positive semiaxis

V. Katsnelson

Department of Mathematics, The Weizmann Institute, 76100, Rehovot, Israel

Abstract: The truncated Fourier operator $\mathscr F_{\mathbb R^+}$,
\begin{equation*} (\mathscr F_{\mathbb R^+}x)(t)=\frac1{\sqrt{2\pi}}\int_{\mathbb R^+}x(\xi)e^{it\xi} d\xi,\quad t\in\mathbb{R^+}, \end{equation*}
is studied. The operator $\mathscr F_{\mathbb R^+}$ is viewed as an operator acting in the space $L^2(\mathbb R^+)$. A functional model for the operator $\mathscr F_{\mathbb R^+}$ is constructed. This functional model is the operator of multiplication by an appropriate ($2\times2$)-matrix function acting in the space $L^2(\mathbb R^+)\oplus L^2(\mathbb R^+)$. Using this functional model, the spectrum of the operator $\mathscr F_{\mathbb R^+}$ is found. The resolvent of the operator $\mathscr F_{\mathbb R^+}$ is estimated near its spectrum.

Keywords: truncated Fourier–Plancherel operator, functional model for a linear operator.

Full text: PDF file (239 kB)
First page: PDF file
References: PDF file   HTML file

Document Type: Article
Received: 27.10.2017
Language: English

Citation: V. Katsnelson, “A functional model for the Fourier–Plancherel operator truncated to the positive semiaxis”, Algebra i Analiz, 30:3 (2018), 93–111

Citation in format AMSBIB
\Bibitem{Kat18}
\by V.~Katsnelson
\paper A functional model for the Fourier--Plancherel operator truncated to the positive semiaxis
\jour Algebra i Analiz
\yr 2018
\vol 30
\issue 3
\pages 93--111
\mathnet{http://mi.mathnet.ru/aa1597}
\elib{http://elibrary.ru/item.asp?id=32855066}


Linking options:
  • http://mi.mathnet.ru/eng/aa1597
  • http://mi.mathnet.ru/eng/aa/v30/i3/p93

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Алгебра и анализ St. Petersburg Mathematical Journal
    Number of views:
    This page:28
    References:4
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018