THEOREM 23. Let K be an integral operator on L,([a, b], a) Kf = | K(x, y)f(y) da(y) %3D where | |K(x, y) doa(x) da(y) < o. Then K is a compact operator.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Need prove of theorem
THEOREM 23. Let K be an integral operator on L2([a, b], a)
KS = [ K<=.
K(x,
y)S(y) da(y)
%3D
where
|| |K(x, y)|* da(x) da(y) < 0.
2
Then K is a compact operator.
Transcribed Image Text:THEOREM 23. Let K be an integral operator on L2([a, b], a) KS = [ K<=. K(x, y)S(y) da(y) %3D where || |K(x, y)|* da(x) da(y) < 0. 2 Then K is a compact operator.
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