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Algebra i Analiz, 2010, Volume 22, Issue 4, Pages 1–20 (Mi aa1195)  

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

Research Papers

On perturbations of the isometric semigroup of shifts on the semiaxis

G. G. Amosova, A. D. Baranovb, V. V. Kapustinc

a Moscow Institute of Physics and Technology, Moscow, Russia
b St. Petersburg State University, St. Petersburg, Russia
c St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: Perturbations $(\widetilde\tau_t)_{t\ge0}$ of the semigroup of shifts $(\tau_t)_{t\ge 0}$ on $L^2(\mathbb R_+)$ are studied under the assumption that $\widetilde\tau_t-\tau_t$ belongs to a certain Schatten–von Neumann class $\mathfrak S_p$ with $p\ge1$. It is shown that, for the unitary component in the Wold–Kolmogorov decomposition of the cogenerator of the semigroup $(\widetilde\tau_t)_{t\ge0}$, any singular spectral type may be achieved by $\mathfrak S_1$-perturbations. An explicit construction is provided for a perturbation with a given spectral type, based on the theory of model spaces of the Hardy space $H^2$. Also, it is shown that an arbitrary prescribed spectral type may be obtained for the unitary component of the perturbed semigroup by a perturbation of class $\mathfrak S_p$ with $p>1$.

Keywords: semigroup of shifts, trace-class perturbation, Schatten–von Neumann ideals, Hardy space, inner function.

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English version:
St. Petersburg Mathematical Journal, 2011, 22:4, 515–528

Bibliographic databases:

Received: 20.01.2010

Citation: G. G. Amosov, A. D. Baranov, V. V. Kapustin, “On perturbations of the isometric semigroup of shifts on the semiaxis”, Algebra i Analiz, 22:4 (2010), 1–20; St. Petersburg Math. J., 22:4 (2011), 515–528

Citation in format AMSBIB
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\by G.~G.~Amosov, A.~D.~Baranov, V.~V.~Kapustin
\paper On perturbations of the isometric semigroup of shifts on the semiaxis
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 4
\pages 1--20
\mathnet{http://mi.mathnet.ru/aa1195}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2768959}
\zmath{https://zbmath.org/?q=an:1219.47059}
\transl
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 4
\pages 515--528
\crossref{https://doi.org/10.1090/S1061-0022-2011-01156-2}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871375745}


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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. G. G. Amosov, A. D. Baranov, V. V. Kapustin, “O primenenii modelnykh prostranstv dlya postroeniya kotsiklicheskikh vozmuschenii polugruppy sdvigov na polupryamoi”, Ufimsk. matem. zhurn., 4:1 (2012), 17–28  mathnet  mathscinet  elib
    2. Amosov G.G., “O postroenii vozmuschenii polugruppy sdvigov na polupryamoi s ispolzovaniem teorii modelnykh prostranstv”, Kompleksnyi analiz i prilozheniya (VI Petrozavodskaya mezhdunarodnaya konferentsiya), Petrozavodskii gos. universitet, 2012, 3  elib
    3. Dil'nyi V.M., “On Invariant Subspaces in Weighted Hardy Spaces”, Ukr. Math. J., 66:6 (2014), 955–960  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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