Let be the vector space of "smooth" functions, i.e., real-valued functions in the variable that have infinitely many derivatives at all points .
Let and be the linear transformations defined by the first derivative and the second derivative .
Determine whether the smooth function is an eigenvector of . If so, give the associated eigenvalue. If not, enter
NONE
.
Eigenvalue =
Determine whether the smooth function is an eigenvector of . If so, give the associated eigenvalue. If not, enter
NONE
.
Eigenvalue =
You can earn partial credit on this problem.