Question

Compute the adjoint of the volterra operator v and v+v^* what is ran(v+ v^*)

Answer 1

I want to find the transpose of the Volterra operator

I want to find the transpose of the Volterra operatorVf(x)=∫x0f(t)dt,x∈(0,1)

I want to find the transpose of the Volterra operatorVf(x)=∫x0f(t)dt,x∈(0,1)acting in V:L2(0,1)→V:L2(0,1). The transpose is defined as M′:U′→V′. For Hilbert spaces the transpose is replaced by the adjoint. I would guess that the transpose is also a map M′:L2(0,1)→L2(0,1) Since L2 is self dual. But how do I find the map?

Answer 2

Answer:

your answer is in the attachment

Explanation:

hope it's help you XD