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If $T=-d^2/dx^2$ is defined on the domain $D(T)=\{f\in C^2[0,1]: f(1)=f'(0)=f'(1/2)=0\}\subset L^2(0,1)$. What's the Hilbert adjoint operator $T^*$?

Many many thanks for your answers.

Math.

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  • 2
    $\begingroup$ What have you tried? $\endgroup$ – MisterRiemann Apr 30 at 18:34
  • $\begingroup$ Well, I thought it should be $D(T^*)=\{f\in H^2(0,1): f(1)=f'(0)=0\}$ but in a paper where they treat a similar question , they find $D(T^*)=\{f\in H^2(0,1): f(1)=f'(0)=f'(1/2)=0\}$. $\endgroup$ – Math Apr 30 at 18:59
  • $\begingroup$ Any answer guys? $\endgroup$ – Math May 1 at 19:13

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