Geodesic
The Szeg\"o function on a~non-rectifiable arc
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 12-23

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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 $\Gamma$.
Mots-clés : non-rectifiable arc, distribution, Cauchy transform.
Keywords: Riemann boundary value problem, Szegö function 
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     author = {B. A. Kats and D. B. Kats},
     title = {The {Szeg\"o} function on a~non-rectifiable arc},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--23},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_4_a1/}
}
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B. A. Kats; D. B. Kats. The Szeg\"o function on a~non-rectifiable arc. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 12-23. http://geodesic.mathdoc.fr/item/IVM_2012_4_a1/