Advances in Theoretical and Mathematical Physics
Volume 16 (2012)
Momentum transforms and Laplacians in fractional spaces
Pages: 1315 – 1348
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.