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Adjoint linear operator

  • #1
If L is the following first-order linear differential operator
L = p(x) d/dx
then determine the adjoint operator L* such that
integral from (a to b) [uL*(v) − vL(u)] dx = B(x) |from b to a|
What is B(x)?

sorry.. on my book theres only self-adjointness

i dont quiet understand what is the adjoint liear operator.

may someone solve this problem and tell me what exactly adjoint linear operator is ?
 

Answers and Replies

  • #2
Fredrik
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The adjoint [itex]A^\dagger[/itex] of a linear operator [itex]A[/itex] is defined by [itex]\langle x,Ay\rangle=\langle A^\dagger x,y\rangle[/itex]. Physicists write the adjoint as [itex]A^\dagger[/itex], mathematicians write it as [itex]A^*[/itex]. A is self-adjoint if [itex]A^\dagger=A[/itex].
 
  • #3
The adjoint [itex]A^\dagger[/itex] of a linear operator [itex]A[/itex] is defined by [itex]\langle x,Ay\rangle=\langle A^\dagger x,y\rangle[/itex]. Physicists write the adjoint as [itex]A^\dagger[/itex], mathematicians write it as [itex]A^*[/itex]. A is self-adjoint if [itex]A^\dagger=A[/itex].
how to find the A* then.. sry :(
 

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