View source for Carleman kernel

<!--
c0204201.png
$#A+1 = 6 n = 0
$#C+1 = 6 : ~/encyclopedia/old_files/data/C020/C.0200420 Carleman kernel
Automatically converted into TeX, above some diagnostics.
Please remove this comment and the {{TEX|auto}} line below,
if TeX found to be correct.
-->

{{TEX|auto}}
{{TEX|done}}

A measurable, in general complex-valued, function  $  K (x, s) $
satisfying the conditions: 1)  $  \overline{ {K (x, s) }}\; = K (s, x) $
almost-everywhere on  $  E \times E $, 
where  $  E $
is a Lebesgue-measurable set of points in a finite-dimensional Euclidean space; and 2)  $  \int _ {E} | K (x, s) |  ^ {2}  ds < \infty $
for almost-all  $  x \in E $.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  I.M. [I.M. Glaz'man] Glazman,   "Theory of linear operators in Hilbert space" , '''1–2''' , Pitman  (1980)  (Translated from Russian)</TD></TR></table>