The spectrum of large powers of the Laplacian in bounded domains (original) (raw)

Journal of Physics A: Mathematical and Theoretical, 2008

Abstract

We present exact results for the spectrum of the Nth 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.

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