View source for Hilbert kernel

The kernel of the [[Hilbert singular integral|Hilbert singular integral]], i.e. the function

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047300/h0473001.png" /></td> </tr></table>

The following simple relation holds between the Hilbert kernel and the [[Cauchy kernel|Cauchy kernel]] in the case of the unit circle:

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047300/h0473002.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047300/h0473003.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047300/h0473004.png" />.



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  B.L. Moiseiwitsch,   "Integral equations" , Longman  (1977)</TD></TR></table>