Momentum transforms and Laplacians in fractional spaces

Abstract

We define an infinite class of unitary transformations between position and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian operator. We also introduce a new version of fractional spaces, where coordinates and momenta span the whole real line. In one topological dimension, these results are extended to more general measures.

32 pages, 1 double figure. v2: conclusions extended; v3: minor typos corrected

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