Given the operator defined by

How do I find adjoint of ? I'm totally lost as to how to go about doing this. Thanks in advance!

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- Aug 14th 2012, 12:55 PManegligiblepersonFinding the adjoint
Given the operator defined by

How do I find adjoint of ? I'm totally lost as to how to go about doing this. Thanks in advance! - Aug 14th 2012, 02:43 PMHallsofIvyRe: Finding the adjoint
In an inner product space, the "adjoint" of a linear transformation, A, is the linear transformation A* such that <Au, v>= <u, A*v>. Here the inner product is . So you are looking for A* such that . Do the integrals on the left and find the function A* that makes the right side equal to that. I would suggest using "integration by parts".

- Aug 14th 2012, 03:12 PManegligiblepersonRe: Finding the adjoint
@HallsofIvy, could you be more explicit? I get then I don't know how to proceed.

- Aug 15th 2012, 05:19 AMVlasevRe: Finding the adjoint
You actually obtain

That is

This suggest that you need to write the product in a form with in it. That is, you need to make it look more like and somehow combine the two. I hope this helps.