Dear Professor Bramburger, Thank you for your thorough explanation. I believe I have found an error in your proof that all eigenfunctions are unique. You plugged in the boundary conditions but then concluded that the expression is zero for all x between [a, b], however, the expression is zero only on the boundaries. Sincerely Mahyar
Before I plugged in the boundary values, I showed that the expression is constant for all x in [a,b]. Thus, any choice of x will return the same constant value, which I then used x = a,b to show that the returned value has to be zero.
Super excited that the algorithm helped me find you! Haven’t been this excited since finding Eigen Steve Brunton.
Dear Professor Bramburger,
Thank you for your thorough explanation. I believe I have found an error in your proof that all eigenfunctions are unique. You plugged in the boundary conditions but then concluded that the expression is zero for all x between [a, b], however, the expression is zero only on the boundaries.
Sincerely
Mahyar
Before I plugged in the boundary values, I showed that the expression is constant for all x in [a,b]. Thus, any choice of x will return the same constant value, which I then used x = a,b to show that the returned value has to be zero.