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Oscillating kernel

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A function $ K( x, s) $, $ a \leq x, s \leq b $, such that for any points $ x _ {1} \dots x _ {n} \in [ a, b] $, which (when $ n= 2 $) include at least one interior point, the matrix $ \| K( x _ {i} , x _ {k} ) \| _ {1} ^ {n} $ is an oscillating matrix.

References

[a1] F.R. Gantmakher, M.G. Krein, "Oscillation matrices and kernels and small vibrations of mechanical systems" , Dept. Commerce USA. Joint Publ. Service (1961) (Translated from Russian)
[a2] S. Karlin, "Total positivity" , Stanford Univ. Press (1960)
How to Cite This Entry:
Oscillating kernel. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Oscillating_kernel&oldid=55913
This article was adapted from an original article by V.I. Lomonosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article