ABSTRACT
Let M be a compact oriented n-dimensional manifold. We have seen in chapter 5 that the Laplacian operator A on L2(M) has discrete spectrum, with eigenvalues 0 ^ A0 ^ Ai < A2 ^ • tending to infinity. In this chapter we want to refine this result by asking how many eigenvalues of A lie below a fixed value of A; in other words, we want to study the counting function
01(A) = max{j : Aj ^ A}.
