V. V. Peller, “Hankel operators of class $\mathfrak S_p$ and their applications (rational approximation, Gaussian processes, the problem of majorizing operators)”, Mat. Sb. (N.S.), 113(155):4(12) (1980), 538–581; Math. USSR-Sb., 41:4 (1982), 443

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Mat. Sb. (N.S.), 1980, Volume 113(155), Number 4(12), Pages 538–581 (Mi msb2817)

This article is cited in 85 scientific papers (total in 85 papers)

Hankel operators of class $\mathfrak S_p$ and their applications (rational approximation, Gaussian processes, the problem of majorizing operators)

V. V. Peller

Abstract: A criterion is given for a Hankel operator $H_\varphi\colon H^2\to H^2_-$ ($H_\varphi f=(I-\mathbf P)\varphi f$, where $\mathbf P$ is the orthogonal projection of $L^2$ onto $H^2$) to belong to the Schatten–von Neumann class $\mathfrak S_p$ in terms of its symbol $\varphi$. Various applications are considered: a precise description is obtained for classes of functions definable in terms of rational approximation in the $BMO$ (bounded mean oscillation) norm; it is proved that the averaging projection onto the set of Hankel operators is bounded in the norm of $\mathfrak S_p$, $1<p<+\infty$; a counterexample is given to a conjecture of Simon on the majorization property in $\mathfrak S_p$; a problem of Ibragimov and Solev on stationary Gaussian processes is solved; and a criterion is obtained for functions of an operator in the Sz.-Nagy–Foias model to belong to the class $\mathfrak S_p$.
Bibliography: 47 titles.

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Mathematics of the USSR-Sbornik, 1982, 41:4, 443–479

Bibliographic databases:

UDC: 517.5
MSC: Primary 30D55, 46E35, 47B10, 47B35; Secondary 30E05, 41A20, 41A25, 47D25, 60G10, 60G15
Received: 25.03.1980

Citation: V. V. Peller, “Hankel operators of class $\mathfrak S_p$ and their applications (rational approximation, Gaussian processes, the problem of majorizing operators)”, Mat. Sb. (N.S.), 113(155):4(12) (1980), 538–581; Math. USSR-Sb., 41:4 (1982), 443–479

Citation in format AMSBIB

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\paper Hankel operators of class $\mathfrak S_p$ and their applications (rational approximation, Gaussian processes, the problem of majorizing operators)

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\yr 1980

\vol 113(155)

\issue 4(12)

\pages 538--581

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\jour Math. USSR-Sb.

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\crossref{https://doi.org/10.1070/SM1982v041n04ABEH002242}

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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V. V. Peller, “A description of Hankel operators of class $\mathfrak S_p$ for $p>0$, an investigation of the rate of rational approximation, and other applications”, Math. USSR-Sb., 50:2 (1985), 465–494
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Peller V., “Continuity Properties of the Averaging Projection Onto the Set of Hankel-Matrices”, J. Funct. Anal., 53:1 (1983), 74–83
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