Exercise 6.7. Show that the space of functions analytic in the open unit disk and such that (6.8)...
Show that the function defined by (2)= is analytic on the open unit disk {lz| < 1} and that |(rA) Remark: This function does not extend analytically to any larger open set than the unit disk +o0 as r-1 whenever A is a root of unity Show that the function defined by (2)= is analytic on the open unit disk {lz|
vectors pure and applied Exercise 11.3.1 Let Co(R) be the space of infinitely differentiable functions f R R. Show that CoCIR) is a vector space over R under pointwise addition and scalar multiplication. Show that the following definitions give linear functionals for C(R). Here a E R. (i)8af f (a). minus sign is introduced for consistency with more advanced work on the topic of 'distributions'.) f(x) dx. (iii) J f- Exercise 11.3.1 Let Co(R) be the space of infinitely differentiable...