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)