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For a domain Ω ⊂ C, the Kerzman-Stein operator is the skewhermitian part of the Cauchy operator acting on L(bΩ), which is defined with respect to Euclidean measure. In this paper we compute the spectrum of the Kerzman-Stein operator for three domains whose boundaries consist of two circular arcs: a strip, a wedge, and an annulus. We also treat the case of a domain bounded by two logarithmic spi...
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We establish an elementary lower estimate for the norm of the Kerzman-Stein operator for a smooth, bounded domain. The estimate involves the boundary length and logarithmic capacity. The estimate is tested on model domains for which the norm is known explicitly. It is shown that the estimate is sharp for an annulus and a strip, and is asymptotically sharp for an ellipse and a wedge.
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2010
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1001001d