On calculation of the Laplace transformation of the Heisenberg operators in finite-dimensional spaces

The integral H tilde (lambda) = ∫sub(0)sup(infinity) dt exp[-(lambda-iF)t]Xexp(-iHt) and the solution of the matrix equation iX tilde (lambda)H+(lambda-iF)Xtilde (lambda)=X, where F and H are hermitian matrices with dimensions M and N, respectively, are represented as a polynomial of the (M-1) degree in F and of the (N-1) degree in H whose coefficients are found from the characteristic polynomials of the F and H matrices