Introduction to Partial Differential Equations
Exercise Sheet 10
Ross Ogilvie 4th November,
2024
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In this question we expand on some details from Section 4.1. Recall that the Fourier transform of a function is defined to be a function given by
Lemma 4.3 shows that it is well-defined for Schwartz functions.
By changing to polar coordinates, compute this integral. (1 point)
Prove the following identity for the fundamental solution in one dimension ():
(2 points)
Hint. You may use without proof that