The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the N th power of the Laplacian in a bounded domain. We begin with the one-dimensional case and show that the whole spectrum can be obtained in the limit of large N . We also show that it is a useful numerical approach valid for any N . Finally, we discuss implications of this work and present its possible extensions for non-integer N and for 3D Laplacian problems.