We define an infinite class of unitary transformations between configuration 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.
Nardelli, G., Calcagni, G., Momentum transforms and Laplacians in fractional spaces, <<ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS>>, 2012; 2012 (16/4): 1315-1348. [doi:10.4310/ATMP.2012.v16.n4.a5] [http://hdl.handle.net/10807/43789]
Momentum transforms and Laplacians in fractional spaces
Nardelli, Giuseppe;Calcagni, Gianluca
2012
Abstract
We define an infinite class of unitary transformations between configuration 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.
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