SPECTRAL SHIFT FUNCTION FOR OPERATORS WITH CROSSED MAGNETIC AND ELECTRIC FIELDS

We obtain a representation formula for the derivative of the spectral shift function xi(lambda; B, epsilon) related to the operators H(0)(B, epsilon) = (D(x) - By)(2) + D(y)(2) + epsilon x and H(B, epsilon) = H(0)(B, epsilon) + V (x, y), B > 0, epsilon > 0. We establish a limiting absorption principle for H(B, epsilon) and an estimate O(epsilon(n-2)) for xi'(lambda; B, epsilon), provided lambda is not an element of sigma(Q), where Q = (D(x) - By)(2) + D(y)(2) + V (x, y).