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How can you show that an operator is symmetric with robin boundary conditions?

I know I need to show that < Tf,g > = < f,Tg >; however, the robin boundary conditions are throwing me off.

This is my problem:

Show that d^2/dx^2 is a symmetric operator on

V={f is a set member on C^2[0,pi] : f'(0)-a(0)f(0) = 0 = f'(pi) + a(pi)f(pi)} where a(0) and a(pi) are fixed real constants.

edited Nov 19 at 19:15

asked Nov 19 at 18:00

Nick
1●1

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Write out the explicit boundary term $\langle T f, g \rangle - \langle f, T g\rangle$ for general $f$ and $g$. Substitute in the Robin boundary conditions. What boundary condition on $g$ is sufficient for the boundary term to vanish? – Igor Khavkine Nov 19 at 19:45

Delio Mugnolo · Answer 1 · 2012-11-21 19:52:08Z UTC

2

just three words: integration by parts.

answered Nov 21 at 19:52

Delio Mugnolo
629●1●7

Symmetric Operators Robin Boundary Conditions

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