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Carleman kernel

From Encyclopedia of Mathematics
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A measurable, in general complex-valued, function $ K (x, s) $ satisfying the conditions: 1) $ {K (x, s) } bar = 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)
How to Cite This Entry:
Carleman kernel. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Carleman_kernel&oldid=46208
This article was adapted from an original article by B.V. Khvedelidze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article