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I).Show that if Aˆ is a Hermitian operator in a function space, then so is the operator Aˆn , where n is any positive integer.

I).Show that if Aˆ is a Hermitian operator in a function space, then so is the operator Aˆn , where n is any positive integer.

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I).Show that if Aˆ is a Hermitian operator in a function space, then so is the operator Aˆn
, where n is any positive integer.

ii).Now consider a function space of the set of functions f(x) of a real variable x ∈ (−∞, +∞),
such that f(x) → 0 as x → ±∞. For a unit weight function w(x) = 1, determine if the
following operators are Hermitian:
i) id/dx
, and
ii) id5/dx5
.

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