Introduction to Partial Differential Equations
Exercise Sheet 6
Ross Ogilvie 7th October,
2024
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The convolution of two functions is defined by
(2 points)
is in fact a distribution on using part (a) and Definition 2.14 directly. (1 point)
defines a distribution in . Note that the indicates this is an integration over the submanifold . Does there exist a locally integrable function with
for all ? (Hint. Use Lemma 2.15) (2 Points + 2 Bonus Points)