Chem Differential Eq HW Solutions Fall 2011 123

Chem Differential Eq HW Solutions Fall 2011 123 - inverse...

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Section 7.5 A Dirichlet Problem and the Poisson Integral Formula 123 Since lim y 0 e - y | w | = 1, it follows that lim y 0 F ( P y * f )( w ) = lim y 0 e - y | w | F ( f )( w )= F ( f )( w ) . Taking inverse Fourier transforms, we see that lim y 0 P y * f ( x )= f ( x ). The argument that we gave is not rigorous, since we did not justify that the
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Unformatted text preview: inverse Fourier transform of a limit of functions is the limit of the inverse Fourier transforms....
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