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7.5 Approximation by polynomials
129
is a multiindex, denoting
∂
(1
,
2)
=
∂
∂x
1
∂
2
∂x
2
2
, etc.)
Deﬁnition 7.5.19.
Call
E
a fundamental solution of
P
iﬀ
PE
=
δ
. (What is
E
?)
Then a solution of
Pu
=
f
can be found by convolving with
E
:
P
(
E
*
f
) =
PE
*
f
by the magic property
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Unformatted text preview: = δ * f E is a fund. soln. = f δ is the identity for * , so that u = E * f is a solution. Note also that E * ( Pu ) = E * f = u , so that E is a left and right inverse for P ....
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This note was uploaded on 11/26/2011 for the course MAT 4944 taught by Professor Wong during the Fall '11 term at FSU.
 Fall '11
 Wong
 Polynomials, Approximation

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