The extended eigenvalues of composition operator on Bergman space and Fock space

A complex scalar k is said to be an extended eigenvalue of a bounded linear operator A on a complex Hilbert space if there is a nonzero operator X such that AX=kXA. There are some solutions to the problem of computing the extended eigenvalues for composition operators induced on the Fock space and Bergman space by linear fractional transformationsof the complex plane in this paper.