Consider the differential equation -u +u = f. (a) If L(T), use Fourier series...

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Consider the differential equation -u" +u = f. (a) If ƒ € L²(T), use Fourier series to show that there is unique solution u € H²(T). (b) Show that u = G* f for a suitable function G (called the Green's func- tion). (c) Show that GE H*(T) for s < 3/2. Consider the differential equation -u" +u = f. (a) If ƒ € L²(T), use Fourier series to show that there is unique solution u € H²(T). (b) Show that u = G* f for a suitable function G (called the Green's func- tion). (c) Show that GE H*(T) for s < 3/2.

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