Intro to Analysis in-class_Part_62

Intro to Analysis - = 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

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7.5 Approximation by polynomials 129 is a multi-index, 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.

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