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- Jan 26, 2012

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**Problem**: Let $V:L^2([0,1])\rightarrow L^2([0,1])$ be the operator defined by $Vf(x) = \displaystyle\int_0^x f(t)\,dt$ for all $f\in L^2([0,1])$. This is known as the

**Volterra operator**.

(a) Show that $V$ has no nonzero eigenvalues.

(b) Compute $V^{\ast}$, the adjoint of $V$.

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