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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 4, Pages 12–23 (Mi ivm8590)  

This article is cited in 1 scientific paper (total in 1 paper)

The Szegö function on a non-rectifiable arc

B. A. Kats, D. B. Kats

Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: Let $\Gamma$ be a simple Jordan arc in the complex plane. The Szegö function, by definition, is a holomorphic in $\mathbb C\setminus\Gamma$ function with a prescribed product of its boundary values on $\Gamma$. The problem of finding the Szegö function in the case of piecewise smooth $\Gamma$ was solved earlier. In this paper we study this problem for non-rectifiable arcs. The solution relies on properties of the Cauchy transform of certain distributions with the support on $\Gamma$.

Keywords: non-rectifiable arc, Riemann boundary value problem, Szegö function, distribution, Cauchy transform.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:4, 9–18

Bibliographic databases:

UDC: 517.544
Received: 10.05.2011

Citation: B. A. Kats, D. B. Kats, “The Szegö function on a non-rectifiable arc”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 4, 12–23; Russian Math. (Iz. VUZ), 56:4 (2012), 9–18

Citation in format AMSBIB
\Bibitem{KatKat12}
\by B.~A.~Kats, D.~B.~Kats
\paper The Szeg\"o function on a~non-rectifiable arc
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 4
\pages 12--23
\mathnet{http://mi.mathnet.ru/ivm8590}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076537}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 4
\pages 9--18
\crossref{https://doi.org/10.3103/S1066369X12040020}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862737639}


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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. B. A. Kats, “Riemann boundary-value problem for holomorphic matrices on non-rectifiable curve”, Russian Math. (Iz. VUZ), 61:2 (2017), 17–27  mathnet  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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