Difference between revisions of "Carleman kernel"
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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==== | ====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> | <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> | ||
Revision as of 11:17, 30 May 2020
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=14808
Carleman kernel. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Carleman_kernel&oldid=14808
This article was adapted from an original article by B.V. Khvedelidze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article