Carleman kernel

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

[1]	I.M. [I.M. Glaz'man] Glazman, "Theory of linear operators in Hilbert space" , 1–2 , Pitman (1980) (Translated from Russian)