Unformatted text preview: 3. Find the adjoint problem of x 2 y 00xy + 3 y = 0 , y (1) = y (2) = 0 . Is it selfadjoint? 4. Consider the linear operator L [ y ] = y (4) , deﬁned on the set of functions having continuous derivatives up to order 4, that satisfy the following periodic boundary conditions: y ( i ) (0) = y ( i ) (1) , i = 0 , 1 , 2 , 3 . Show that L is selfadjoint, ie show that ( L [ y 1 ] , y 2 ) = ( y 1 , L [ y 2 ]) for all y 1 and y 2 in the domain of L where ( y 1 , y 2 ) denotes the usual inner product of the functions y 1 and y 2 . * Instructor: Patrick De Leenheer. 1...
View
Full Document
 Summer '06
 DeLeenheer
 Hermite, Hn, following eigenvalue problem, smallest positive eigenvalue

Click to edit the document details