Difference between revisions of "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|oscillating matrix]]. | ||
====Comments==== | ====Comments==== | ||
| − | |||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> 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)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> S. Karlin, "Total positivity" , Stanford Univ. Press (1960)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> 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)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> S. Karlin, "Total positivity" , Stanford Univ. Press (1960)</TD></TR></table> | ||
Revision as of 08:04, 6 June 2020
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.
Comments
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=48084
Oscillating kernel. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Oscillating_kernel&oldid=48084
This article was adapted from an original article by V.I. Lomonosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article